AFRL-IF-RS-TR-1999-222 Final Technical Report October 1999

SPREAD SPECTRUM INTERFERENCE MITIGATION WITH VARIABLE PROCESSING GAIN

Rensselaer Polytechnic Institute

Gary J. Saulnier and Zhong Ye

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13. ABSTRACT {Maximum 200 words) Designing a spread spectrum signal for the worst-case channel conditions can be wasteful of system resources such as bandwidth and network throughput capacity. This report focuses on the performance of spread spectrum system based on multi-carrier modulation, also known as Orthogonal Frequency Division Multiplexing (OFDM), which provides variable processing gain by adjusting the redundancy in the signal in response to the channel conditions. A signal structure based on OFDM is defined and a technique for adapting the signal properties, including the data rate, in response to channel conditions and/or transmission requirements, is developed. Analytical and simulation results demonstrate that the signaling format can maintain a desired error rate performance over a wide range of channel conditions. The report also considers the impact of this variable signaling scheme on the upper layers of the network and, in particular, the data link layer. Classic throughput analysis for fixed and random access schemes is extended for this proposed adaptive packet radio network. The focus in on pure- ALOHA and non-persistent CSMA (NP-CSMA) systems. A large improvement in throughput is demonstrated for the adaptive system, as compared to a conventional fixed rate system, for various mobile user population

profiles and radio propagation path loss models.

14. SUBJECT TERMS

Multipath, OFDM, Wireless Network

Multi-Carrier, Spread Spectrum, Variable Processing Gain,

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18. SECURITY CLASSIFICATION OF THIS PAGE

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19. SECURITY CLASSIFICATION OF ABSTRACT

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15. NUMBER OF PAGES

118 16. PRICE CODE

20. LIMITATION OF ABSTRACT

UL Standard Form 298 (Rev. 2-89) (EG) Pnicribad b» »NSI Sti 239.18 - ' gPtrfcnnPro.WHSIOIOR,Ocl»4

Contents

1 Introduction '

1.1 Overview '

1.2 Publications 8

1.3 Report Organization 9

2 Survey of Communications Systems for Packet Radio Net-

works 2.1 Characteristics of Tactical Wireless Communications Channels 13

2.1.1 Multipath . 15

2.1.2 Multipath Mitigation Techniques 21

2.1.3 Intentional Interference 26

2.2 OFDM 27

2.2.1 Conventional OFDM 27

2.2.2 Spread Spectrum OFDM 28

2.2.3 Equalization of OFDM signals 31

2.2.4 Rate Adaptive Schemes . . . 34

2.3 Wireless Networks 37

2.3.1 802.11 37

3 The RA-OFDM System 41

3.1 Introduction 41

3.2 RA-OFDM Receiver 44

3.3 Contrast with other Rate Adaptive Approach 47

3.3.1 Channel Capacity, AWGN Channel, High SNR .... 47

3.3.2 Channel Capacity, AWGN Channel, Low SNR 51

3.4 Simulation Models 55

3.5 Results 59

3.5.1 AWGN and Time-Invariant Multipath Channel .... 59

3.5.2 Rate Adaptation over Time-Varying Frequency Selec-

tive Fading Channels 60

3.5.3 Rate Adaptation over Frequency Non-selective Rayleigh

Fading Channels 62

3.6 Discussion 65

4 Adaptive Signaling with Packet Radio Network 76

4.1 Introduction 76

4.2 RA-OFDM System for Packet Radio Networks 78

4.3 Throughput Analysis of the Adaptive Packet Radio Networks 80

4.3.1 Network Throughput Analysis, Downlink (base-to-mobile)

using TDM 80

4.3.2 Network Throughput Analysis for Pure-ALOHA Adap-

tive PRN 85

4.3.3 Pure-ALOHA, Different Path Loss Models and User

Population Profile 88

4.3.4 Network Throughput Analysis for Nonpersistent CSMA

Adaptive PRN 93

4.4 Conclusion 100

5 Conclusion 103

Bibliography 104

List of Tables

4.1 Adaptive system parameters for seven-ring structure 82

4.2 Fixed rate system parameters for seven-ring structure 82

List of Figures

2.1 Relationship between 0c(A/) and </>C(T) 17

2.2 Relationship between 0c(At) and Sc(A) 19

2.3 Doppler power spectrum based on Jakes model 20

2.4 Frequency selective fading channel 22

2.5 OFDM using FFT 29

2.6 Block Diagram of an OFDM Spread Spectrum System .... 30

2.7 Adding the Cyclic Prefix 31

2.8 Conventional Least-Mean-Squared (LMS) equalizer 33

2.9 Fixed rate system vs. adaptive system with variable constel-

lation 36

3.1 Conventional OFDM System 42

3.2 Variable Processing Gain OFDM 43

3.3 Block Diagram of a RA-OFDM receiver with glitch-free switch-

ing between processing gain. Here the processing gain is M

and K symbols are sent simultaneously 46

3.4 The multicarrier modulation system 48

3.5 Throughput of adaptive processing gain system, at low SNR

case 54

3.6 Signal frame format for the RA-OFDM system 56

3.7 Block diagram for RSSI and BER switching system 67

3.8 M-state Markov chain modeling a Rayleigh fading channel . . 68

4

3.9 Rate adaptation with cyclical prefix 68

3.10 Equalizer performance with realistic packet structure 69

3.11 BER performance for a 4-ray selective fading channel, /D=50Hz 70

3.12 BER performance for a 8-ray selective fading channel, /D=50Hz 71

3.13 Maximum achievable diversity from various channel models . . 72

3.14 Reed-Solomon coded OFDM spread spectrum system in Rayleigh

fading, FFT block size=64, (n,k)=(63,32), Pg=16 73

3.15 Maximum normalized throughput with fixed rate and RA-

OFDM transmission schemes 74

3.16 Maximum normalized throughput with fixed rate and RA-

OFDM transmission schemes at different Doppler rate 75

4.1 Processing gain selection procedure 79

4.2 Linear versus flat user population profiles 84

4.3 Throughput analysis, ALOHA system, moderate channel er-

ror, Pb = 10-6 at ring 7 • 87

4.4 Throughput analysis, ALOHA system, high channel error,

Pb = 10-3 at ring 7, N=128 88

4.5 Throughput analysis, ALOHA system, almost error free chan-

nel, Pb = 10'12 at ring 7 89

4.6 ALOHA system throughput with various path loss factors . . 90

4.7 ALOHA system throughput with various user population profile 91

4.8 ALOHA system throughput breakdown with ring index, flat

vs. linear user profile 92

4.9 Throughput analysis, CSMA system, moderate channel error,

Pb = 10~6 at ring 7 96

4.10 Throughput analysis, CSMA system, high channel error, Pb =

10-3 at ring 7, N=128 . . . 97

4.11 Throughput analysis, CSMA system, almost error free chan-

nel, Pb = 1(T12 at ring 7 98

4.12 Throughput analysis, CSMA system, various user profile ... 99

4.13 Throughput analysis, CSMA system, various path loss model 100

4.14 Throughput-Load of CSMA under various propagation time,

linear user profile 101

4.15 Throughput-Load of CSMA under various propagation time,

flat user profile 102

Chapter 1

Introduction

1.1 Overview

The primary objective of this effort was to develop techniques for using multi-

carrier modulation, also known as Orthogonal Frequency Division Multiplex-

ing (OFDM), to provide variable data rate communications through a chan-

nel characterized by multipath and interference. The investigation included

both analysis and simulation-based performance evaluation. The new tech-

niques were implemented using the Signal Processing WorkSystem (SPW)

from the Alta Group of Cadence Design Systems. Both analytical results

and Monte Carlo simulation were used to characterize system behavior and

to obtain and verify performance results.

The investigation focused on two major areas. Initial work focused on the

physical layer of the network. A signal structure based on OFDM was defined

and a technique for adapting the signal properties, including the data rate, in

response to channel conditions and/or transmission requirements, was devel-

oped. In particular, in a favorable channel, the system would operate much

like the conventional OFDM system where different data bits are transmit-

ted on different carriers yielding high throughput. In a severe interference

channel, the system would operate like the spread spectrum OFDM system,

in which the spectral spreading is accomplished by putting the same data

on all the carriers, sacrificing throughput to provide the needed processing

gain to overcome the jamming. In most cases, the system would operate be-

tween these two extremes, providing sufficient processing gain to mitigate the

channel effects while maximizing throughput. The behavior of the control

strategy across large variation of channel conditions was studied.

The second area of the investigation studied the impact of this variable

signaling scheme on the upper layers of the network, in particular, the focus

was on throughput optimization from the data link layer point of view. Clas-

sic throughput analysis for fixed and random access schemes was extended

for this proposed adaptive packet radio network. The focus was on pure-

ALOHA and nonpersistent CSMA (NP-CSMA) systems. A large improve-

ment in throughput is demonstrated for the adaptive system, as compared to

the conventional fixed rate system, for various mobile user population profiles

and radio propagation path loss models.

As a result of this effort, the adaptive signaling scheme based on OFDM

was not only able to deliver excellent BER performance, a critical benchmark

in any physical layer criterion, but much more importantly, it was able to

boost the throughput from the network point of view and increase the total

resource utilization tremendously.

1.2 Publications

A number of publications have resulted from this effort:

• Saulnier, G. J., Ye, Z. and Medley, M. J., "Performance of a Spread

Spectrum OFDM System in a Dispersive Fading Channel with Interfer-

ence" , Conference Record of the IEEE Military Communications Con-

ference, October, 1998.

8

• Saulnier, G. J., Ye, Z. and Medley, M. J., "Joint Interference Suppres-

sion and Multipath Mitigation in Direct Sequence and OFDM Spread

Spectrum Systems", Conference Record of Seventh Communication

Theory Mini-Conference, November, 1998.

• Ye, Z., Saulnier, G. J., Lee, D. and Medley, M. J., "Anti-jam, Anti-

Multipath Adaptive OFDM Spread Spectrum System", Conference

Record of Thirty Second Annual Asilomar Conference on Signals, Sys-

tems and Computers, November, 1998.

• Saulnier, G. J., Ye, Z., Vastola, K. S. and Medley, M. J., "Throughput

Analysis for a Packet Radio Network Using Variable Rate OFDM Sig-

naling" , Conference Record of the IEEE International Conference on

Communications, June, 1999.

• Saulnier, G. J., Ye, Z., Lee, D. and Medley, M. J., "A Rate-Adaptive

Coded OFDM (RA-OFDM) Spread Spectrum System for Tactical Ra-

dio Networks", Conference Record of Eighth Communication Theory

Mini-Conference, June, 1999.

1.3 Report Organization

The remainder of the report consists of four chapters. Chapter 2 presents

a survey of communication systems for packet radio networks. Character-

istics of the Tactical Wireless Communications Channels are outlined and

the corresponding channel models for this effort are defined. Since the whole

effort was oriented toward using an OFDM-based scheme for a packet radio

network, the remainder of the chapter is dedicated to thoroughly introducing

OFDM and its variants as well as packet radio network issues.

The rate adaptive OFDM modulation scheme is introduced in Chap-

ter 3. It is compared to other conventional rate adaptation approaches and

9

presented as a unifying modulation across a large range of channel condi-

tions. The adaptation scheme as well as the packet structure are then in-

troduced. System performance results for a variety of channel conditions

including AWGN, static multipath, time-varying frequency selective and fre-

quency non-selective Rayleigh fading show that a desired BER performance

can be maintained through adjustment of the processing gain.

Chapter 4 extends the contribution of the adaptive signaling beyond the

physical layer. Throughput analysis of the proposed adaptive packet ra-

dio network is performed. The focus is on simple access schemes such as

pure-ALOHA and non-persistent CSMA. The great potential of the adaptive

signaling is demonstrated and it serves as a door opener to a domain of new

research opportunity.

Finally, Chapter 5 presents a summary of the work presented in this

report.

10

Chapter 2

Survey of Communications

Systems for Packet Radio

Networks

Almost two decades have passed since the first generation mobile cellular

telecommunication services using analog frequency modulation/frequency di-

vision multiple access (FM/FDMA) started. Today, in addition to analog

systems, the second generation digital cellular systems are in widespread

use. The technical motivation for the first and second generation mobile

cellular networks was mainly to increase system capacity for voice services.

At the turn of the century, we are experiencing the ever expanding use of

the Internet with a rapid growth of people's need for multimedia commu-

nications services including voice, data and images. How to deliver high

speed and reliable multimedia traffic to people anywhere and anytime has

become the technical challenge as the third and fourth generation mobile

telecommunication systems evolve.

The need for moving from legacy analog systems to state-of-the-art dig-

ital systems is even more urgent in the military world. Victory in the 21st

11

Century battlespace will be characterized by the effective leveraging of infor-

mation technology to rapidly mass the effects of dispersed firepower, rather

than relying exclusively on the physical massing of weapons and forces that

was the primary method employed in the past. Digitization is a means to

that end.

Digitization allows the warrior to communicate vital battlefield informa-

tion instantly, rather than through a slow voice radio or even slower liaison

efforts. It provides the warrior with a horizontally and vertically integrated

digital information network that supports unity of battlefield fire and maneu-

vers and assures command and control decision-cycle superiority. The intent

is to create a simultaneous, appropriate picture of the battlespace based on

common data collected through networks of sensors, command posts, pro-

cessors, and weapon platforms. This allows participants to aggregate rele-

vant information and maintain an up-to-date awareness of what is happening

around them [1].

Both the commercial and military wireless communications systems share

the requirement of delivering high quality, high speed multimedia traffic and

should be highly flexible to accommodate changing traffic patterns as well

as channel conditions. Beside providing a significant level of immunity to

time-varying multipath fading, military systems face a constant challenge

of intentional interference and/or interception. Additionally, they need to

account for the possibility of high priority messages which might require rapid

network access and/or high bandwidth. If a network is expected to operate

in a military environment, it clearly must have some of these attributes.

To provide some perspective, the following is a summary of some of the

requirements for the future tactical wireless networks:

• Support mobility, the ability to communicate while in motion, and

a seamless network that interconnects individual human subscribers

with moving vehicles, with aircraft, and with static and commercial

12

networks.

• Provide secure, survivable low probability of intercept(LPI) and jam

resistant (AJ) capabilities in support of system network operation.

• Provide reliable service in a highly dispersive multipath environment.

• Provide variable Quality of Service (QoS), i.e. accommodate various

services with possibly different priority, data rates, error performance

and delay requirements. The networks should support data traffic and

possibly voice and video traffic.

• High speed, at least comparable to today's Ethernet, with a route for

upgrading to higher speed into the future.

• Low complexity and low power consumption.

• Easy and fast installation and deployment. Little or no site planning

required.

This report first discusses some of the distortions introduced by the chan-

nel and the approaches that are taken to mitigate their effect on performance.

Later, a rate-adaptive modulation scheme is presented as a possible solution

to the physical layer problem in a tactical wireless network. This technique

is evaluated through the use of bit-error-rate performance. Finally, the per-

formance of several network configurations using the rate-adaptive scheme is

investigated and this performance is compared to that of a fixed-rate system.

2.1 Characteristics of Tactical Wireless Com-

munications Channels

The radio channel is the medium for tetherless local transmission. Wireless

networks typically use the microwave frequencies, which occupy the 109 to

13

1012 Hz portion of the frequency spectrum. The effective design, assessment,

and installation of a radio network requires an accurate characterization of

the channel. Having an accurate channel model for each frequency band,

including key parameters and a detailed mathematical model of the channel,

enables the designer or user of a wireless system to predict signal coverage,

achievable data rate, and the specific performance attributes of alternative

signaling and reception schemes. The channel conditions experienced by both

the base stations and/or the mobiles are typically much more severe than

their commercial applications counterparts due to the following reasons:

• Networks can be on the move

• Much higher vehicle speed

• Severe and unpreditable terrain profile

• Intentional jamming

In addition, the following stringent requirements of a military communica-

tions network make an optimum design even more challenging:

• Higher mobility support

• Larger LPI and AJ margin

• Guaranteed delivery of high priority command messages

Interference mitigation is therefore important for military applications.

There are two distinct types of interference that will be encountered within

the network, multipath interference and intentional interference. The follow-

ing studies the models of these interferences.

14

2.1.1 Multipath

Reflection, Diffraction, and Scattering

The signals we send over the air waves get severely distorted between the

transmitter and the receiver due to reflection, diffraction, and scattering.

Reflections of electro-magnetic waves off objects interfere constructively and

destructively with the transmitted wave and with each other. When these ob-

jects are large compared to the wavelength of the electro-magnetic wave, the

multipaths taken by the waves are called reflections. Occasionally, an impen-

etrable object will block the direct line-of-sight path between the transmitter

and the receiver, resulting in only reflected waves reaching the receiver. This

effect, shadow fading, results in the received signal power being less than

the mean expected through path loss computations. When the propagating

wave bounces off small objects on the order of or less than the wavelength of

the propagating wave, the multipath effect is called scattering. Reflection,

diffraction, and scattering are collectively called multipath propagation [2].

Impulse Response

Because the transmitted radio signal propagates along multipaths, a trans-

mitted impulse will be smeared out into a broad impulse response. We can

express the radio channel impulse response at a given instance in time be-

tween a particular transmitter and receiver as the sum of the paths of all the

individual rays take:

h^t) = J2ßi(t)ej^5(t-Ti) (2.1)

where the ßi(t) and <pi(t) represent the amplitude and phase of the i-th path

arriving at delay T{. (2.1) is widely used for statistical modeling of both

indoor and outdoor radio propagation.

15

Evidently, the time variation, called fading, is caused by the interference

between multiple versions of a transmitted signal arriving at slightly different

times. These waves combine noncoherently at the receiver which produce a

resultant signal which can vary widely in phase and amplitude.

Channel Correlation Functions and Power Spectra

We shall now define a number of correlation functions and power spectral

density functions that characterize the fading multipath channel [3].

Assuming the impulse response h(r, t) is wide-sense-stationary, we define

the autocorrelation function of h(r, t) as

</»c(n,r2; At) = ^E[h*{rl-t)h{r2-t + At)]. (2.2)

Most radio transmissions experience so called uncorrelated scattering in which

the scattering at two different delays is uncorrelated. (J>C(TI,T2; At) thus be-

comes </>C(TI; At)5(ri — r2). If we let At = 0, the resulting autocorrelation

function 0c(r, 0) = (J)C(T) is simply the average power output of the channel

as a function of the time delay r and it is called the multipath intensity

profile. The range of values of r over which 4>C(T) is essentially nonzero, is

called the multipath delay spread and is called Tm.

A completely analogous characterization of the time-variant multipath

channel can be done in the frequency domain. Given the channel impulse

response h(r;t), the frequency response H(f;t) is defined as,

/oo h(r;t)e-2^rdT. (2.3)

-00

The correlation in the frequency domain can be defined as

<M/i,/2;At) = i£(tf*(/i;t)tf(/2;t + At)) /oo

0c(ri; At)e-^A^dn = <j>c(Af; At). (2.4) -00

16

0c(A/; At) is called the spaced-frequency, spaced-time correlation function

of the channel. This function is the Fourier transform of the spaced-time

correlation function 0c(r; At).

For a slowly time-varying channel, the value of ^c(A/; At) calculated

with observation times separated by At is the same as that found with no

time separation, i.e. set At = 0 in (2.4). The transform relationship then

becomes, tc(r)e-j2*AfTdT. (2.5)

-OO

The relationship is depicted in Figure 2.1. Since </>c(A/) is an autocorrela-

|«t>c(Af)l Fourier

*c(T)

(Af)c = -t~ ■m Spaced-frequency correlation function

Multipath intensity profile

Figure 2.1: Relationship between </>c(A/) and <£C(T)

tion function in the frequency domain, it provides us with a measure of the

frequency coherence of the channel. Since <f>c{&f) and MT) are a Fourier

transform pair, the reciprocal of the multipath spread is a measure of the co-

herence bandwidth of the channel. The coherence bandwidth is defined as the

frequency separation at which the autocorrelation of the channel frequency

response is essentially zero. The coherence bandwidth is related to the delay

17

spread as follows:

(A/)c « -|- , (2.6) J-rr Lm

where (A/)c is the coherence bandwidth and Tm is the delay spread.

Time variation of the channel is reflected by the parameter At in

</>c(A/; At). This time variation is evidenced as a Doppler broadening and

can be quantized by defining the scattering function Sc(Af; A), as

/oo <f>c(Af- At)e-^XAtdAt. (2.7)

-00

With A/ set to zero, Sc(0; A) becomes 5c(A), a power spectrum that gives

the signal intensity as a function of the Doppler frequency A. The range

of values of A over which Sc (A) is essentially nonzero is called the Doppler

spread fa of the channel. Since Sc (A) is related to (ßc (At) by the Fourier

transform, the reciprocal of /<* is a measure of the coherence time of the

channel. That is,

(At)c « i (2.8) Jd

where (Ai)c is the coherence time of the channel. The relationship is depicted

in Figure 2.2.

Frequency non-selective Fading

There are several statistical models for fading channels, which describe chan-

nel variations using certain probability density functions (pdf). Rayleigh,

Rician, and Nakagami-m fading are some examples. The Rayleigh fading as-

sumes a large number of scatterers in the channel that contribute to the signal

at the receiver, but no dominant line-of-sight (LOS) propagation path. On

the other hand, Rician fading assumes a dominant LOS path. The Nakagami-

m fading is a generalized fading characterized by the parameter m. m = 1

corresponds to Rayleigh fading, m < 1 corresponds to a fading worse than

18

l<t»c(At)| SbW Fourier Sd(X)

Spaced-time correlation function

Doppler power spectrum

Figure 2.2: Relationship between ^c(Ai) and 5C(A)

the Rayleigh case, m > 1 corresponds to Rician fading and m = oo corre-

sponds to additive white Gaussian noise channel [3].

Under most cases of the outdoor mobile communications system, the

propagation path characteristics are considered to be under non line-of-sight

(NLOS) conditions because a terminal is shadowed by the natural terrain and

man-made constructions. Moreover, an NLOS condition is considered to be

more severe than an LOS condition. Therefore, we will use Rayleigh fading

as the non-selective fading channel model for this report. In Rayleigh flat

fading, the channel can be modeled as a single complex multiplying factor

aeje, where the phase 9 is uniformly distributed over [0, 2ir) and a is Rayleigh

distributed. The Rayleigh probability density function is given by

7

P(r) = -jexP ■r >0 (2.9)

Because the channel impulse response is just an impulse in time, the

frequency response is a constant, i.e. non-selective or flat in frequency. This

19

is a good model when the bandwidth of the transmitted signal is much smaller

than the coherence bandwidth of the channel and it is thus accurate to assume

the frequency response of the channel to be constant at a given instant. The

rate at which a and 9 change is determined by the Doppler frequency, or

equivalently, the coherence time.

There are several ways to model a Rayleigh flat fading channel. Most use

a frequency spectrum based on Jakes model,

H(f) <fd

o i/i > /„ A plot of the Jakes filter frequency response is shown in Figure 2.3.

Figure 2.3: Doppler power spectrum based on Jakes model

Frequency Selective Fading

Flat fading characterizes the channel when the arrival time difference be-

tween paths is negligibly small, i.e. the coherence bandwidth is large. How-

20

ever, when the bandwidth of the transmitted signal is very wide, we cannot

neglect the arrival time difference, especially when the time difference be-

comes comparable to a symbol duration. When the delay spread is long

enough that delayed versions of one symbol interferes with the next symbol

when it is sampled, frequency selective fading occurs. The channel frequency

response will no longer be flat as in the flat fading. The longer the delay

spread, the more the frequency response will vary in a given frequency band.

Such a time-varying frequency-selective fading channel model is depicted in

Figure 2.4. The channel consists of multiple rays spaced at sample inter-

vals, Tc, and having a intensity profile determined by oi, ...O,N- Each ray is

independently Rayleigh faded with an adjustable Doppler rate.

2.1.2 Multipath Mitigation Techniques

Many schemes have been developed to help mitigate the effects of multipath,

and some of them are discussed below.

• Spatial diversity is implemented by using multiple receive and/or

transmit antennas. These antennas should be spaced far enough apart

to achieve independence between branches. Ideally, the antennas only

have to be £ apart - but in practice, they are usually separated by

10A. The military has always been interested in single-channel (i.e.

antenna) techniques because they have been generally cheaper, less

complex, smaller in size, and more suitable to rugged military appli-

cations than multichannel techniques [4]. Along the same line, the

commercial wireless community will likely favor techniques that are in-

expensive and simple to implement. For the purpose of this report, we

will exclusively concentrate on single antenna receiver structure.

• Frequency diversity involves independently sending the same infor-

mation over several frequencies simultaneously. If the frequencies are

21

Figure 2.4: Frequency selective fading channel

22

separated by more than the coherence bandwidth, the channels will be

independent from each other, making it very unlikely that they will all

be in a fade at the same moment. For example, the coherence band-

width is on the order of 500kHz in the mobile radio case, thus requiring

that the frequencies be separated by l-2MHz, which makes that fre-

quency diversity much more difficult to obtain using traditional single

carrier systems. Frequency diversity is thus ideally suited for multi-

carrier approach such as OFDM as will be discussed very shortly. By

placing identical data bits on independent subcarriers, frequency diver-

sity is achieved. In addition, frequency diversity is flexible enough to

mesh with other means of diversity within the OFDM system, making

it the focus of choice for this report.

Time diversity involves sending the same information more than once.

The trick is to wait long enough for the channel to have changed be-

fore sending the packet again. From the preceding discussion, the time

spacing between diversity bits should be at least the coherence time to

satisfy this condition. For this reason, time diversity is better suited

for rapidly changing channels and it is often achieved through coding.

For slow fading channels, there will be a significant delay before all

the diversity bits can be processed for a decision to be made. The

delay can be too great for some applications in this case. This limita-

tion motivates us to pursue other means to harness the channel. The

emphasis of this report, i.e. using rate adaptation to exploit the long

term fluctuation of the fading channel is especially effective to han-

dle slow time varying fading channels. In addition, time diversity is

supplemented with additional means of diversity to handle other types

of fading conditions, making it a viable solution for a broad range of

channel conditions.

23

• Polarization diversity depends on the independence between hori-

zontal and vertical polarization paths between the transmitter and the

receiver. Because these are the only two polarizations (vertical and

horizontal), this type of diversity is limited to two branches.

• Adaptive Equalization. This technique has become widely used in

modern microwave point-to-point links and mobile radio systems to

counteract ISI and improve performance [3]. Equalizer hardware can

take many forms, including a tapped delay line structure and a lattice

structure, though the tapped delay line type is most common. In this

case the tapped delay line structure has programmable tap weights

connected to each tap and to a common summing bus. This equalizer

counteracts multipath distortion in the time domain by introducing its

own echoes, whose phases and amplitudes are automatically adjusted

to cancel the ISI produced by the channel. The same fundamental

principle of estimating the ISI and canceling it can be applied to the

transform domain as well, producing frequency domain equalization.

An equalizer generally employs some type of adaptive algorithm to

allow it to follow the variations of the channel. As a consequence, the

rapid channel variations encountered when transmitter and/or receiver

are moving at a high rate make it difficult for the equalizer to perform

well.

• Spread Spectrum. Spread spectrum modulation is naturally tolerant

of multipath if its bandwidth exceeds the coherence bandwidth of the

channel [5]. The spread spectrum signal, in essence, provides frequency

diversity due to its large bandwidth. A RAKE receiver is often used

to exploit the multipath. [6]. The one major drawback to the use of

spread spectrum, at typical WLAN data rates, is the wide bandwidth

occupied by such a signal. This might become a concern for future

24

higher data rate services.

• Multicarrier Modulation. This approach mitigates multipath by

reducing the effective symbol rate "seen" by the channel. It splits

the data into n separate streams, which are then modulated onto a

multiplex of closely-spaced carriers. Hence the symbol rate on each is

reduced by the factor of n, which greatly reduces the ISI.

• Rate Adaptive Transmission. Yet another approach to increase

data rate in the presence of multipath fading is to use a rate adaptive

(RA) modem. A RA modem provides one or more "fallback" modes

of operation for increased reliability of communication under degraded

channel conditions. For example, in an area where we have locations

of good signal quality and others of poor quality, we can operate at

higher data rates in the good location and lower rates at the poor

locations. The idea of rate adaptation can be implemented in various

ways. One way to adjust the data rate with a fixed bandwidth is to

use the multiamplitude and multiphase modulation. In this method,

the number of points in the constellation is increased as the channel

condition improves. The technique is often used in wireline modems.

A second way to implement adaptive data rate is through variable

FEC coding. In this case, the degree of redundancy introduced by

the FEC coding scheme, i.e. the coding rate, is varied according to

the channel conditions. In order to allow reasonable complexity at the

receiver to decode the variable rate code, a rate compatible puncture

code (RCPC) is often used. The third way to implement variable data

rate is to combine the adaptive modulation with the variable coding

scheme. An obvious disadvantage of the variable coding scheme is the

narrow dynamic range of the data rate as constrained by the decoder

complexity. Due to a large power fluctuations in a wireless channel,

25

it is difficult to reliably demodulate signal sets with large numbers of

points without using complex equalization approaches. In addition to

this, the military applications generally require LPI/LPD. All of these

motivate us to implement the rate adaptation in a different way. We

incorporate it with the spread spectrum system where the processing

gain can be adjusted with the environment. Details of the concept will

be introduced in the next section.

2.1.3 Intentional Interference

In this case, an attempt is being made to jam the communications link. The

jamming can take many forms, including continuous tone and partial-band

interference, pulsed tone and partial-band interference, pulsed broadband in-

terference, and frequency chirps. Many interference suppression techniques

have been proposed [7, 8] to improve performance in the presence of different

types of jammers, particularly for direct sequence spread spectrum systems.

For strong interference, it is essential that a selected modulation format be

able to provide interference immunity in excess of its processing gain, mean-

ing that some type of auxiliary interference suppression technique must be

compatible with the modulation format. The interference rejection tech-

niques also need to be adaptive because of the dynamic or changing nature

of interference and channel conditions. The design of an optimum receiver

requires a priori information about the statistics of the data to be processed.

When complete knowledge of the signal characteristics is not available, an

adaptive technique is needed. Given the interference characteristic of the

tactical packet radio networks, we have proposed an adaptive filter structure

that can jointly suppress multipath interference as well as intentional tone

jammer. Essentially, it is an adaptive equalizer in the frequency domain,

which manages to suppress both ISI and ICI caused by the multipath and

26

simultaneously notch out a narrowband jammer by minimizing the mean-

square value of the error signal, which is defined as the difference between

some desired response and the actual filter output [9, 10, 11, 12, 13].

2.2 OFDM

The principles of OFDM were first introduced about 28 years ago [14]. How-

ever, practical interest has only increased recently due in part to advances in

signal processing and microelectronics. In the past, as well as in the present,

this same modulation scheme is referred as multitone, multicarrier, and or-

thogonal frequency division multiplexing communications.

2.2.1 Conventional OFDM

The main idea behind OFDM is to split the data stream to be transmitted

into N parallel streams of reduced data rate and to transmit each of them on

a separate subcarrier. These carriers are made orthogonal by appropriately

choosing the frequency spacing between them. Therefore, spectral overlap-

ping among subcarriers is allowed, since the orthogonality will ensure that the

receiver can separate the OFDM subcarriers, and a better spectral efficiency

can be achieved than by using simple frequency division multiplexing.

In the most general form, the lowpass equivalent OFDM signal can be

written as a set of modulated carriers transmitted in parallel, as follows:

s(t)= £ oo TN-1

n=—oo Y,Cn,k9k{t-nTa) fe=0

(2.10)

with

and

eJ2nfkt 0 < t < Ts

0 otherwise

/* = /„ + £, * = 0..JV-1 (2.12)

27

where CUjk is the symbol transmitted on the k-ih. subcarrier in the n-th signal-

ing interval, each of duration Ts, N is the number of OFDM subcarriers, and

fk is the k-th subcarrier frequency, with /0 being the lowest frequency to be

used. The OFDM modulator and demodulator can be efficiently implemented

by the inverse Fast Fourier Transform (IFFT) and Forward FFT,respectively.

Figure 2.5 shows an OFDM system using a FFT.

Recent advances in digital signal processing (DSP) and very large scale

integrated circuit (VLSI) technologies have paved the way for massive imple-

mentation of OFDM. One successful implementation of OFDM is in digital

audio broadcasting (DAB) [15], which was developed in Europe for terrestrial

and satellite broadcasting of multiple audio programs to mobile receivers.

Another implementation is in asymmetric digital subscriber line (ADSL)

technology that has been selected by ANSI for transmission of digitally com-

pressed video signals over telephone lines [16]. In addition, OFDM has been

adopted as the standard for digital video broadcasting (DVB) [17].

2.2.2 Spread Spectrum OFDM

OFDM can also be used as a spread spectrum modulation (OFDM-SS) [18,

19, 20, 21] wherein spectral spreading is accomplished by putting the same

data on all the carriers, producing a spreading factor equal to the number

of carriers. At the receiver, the energy from all the carriers is coherently

combined to produce the decision variable. Multiple users can be supported

in the same channel through Code Division Multiple Access (CDMA) [22]. In

this case each user has a unique signature sequence which determines the set

of carrier phases. To receive a particular signal, the receiver needs to know

the signature sequence for that user in order to align the carrier phases for the

coherent combining operation. Figure 2.6 is a block diagram of an OFDM-

SS transmitter/receiver pair. As shown in the figure, carrier generation is

28

XXX

1 ■ • 1 \ 1

\\\

IFFl'

/ /v \v

// ///

a- y E. S O &

3 X fD o GO

O P

n srfT

z o V. J w

n EL

1 ?

FFT

TTT

Figure 2.5: OFDM using FFT

usually performed efficiently using an inverse Fast Fourier Transform (FFT)

while demodulation is performed using a forward FFT.

The use of an OFDM spread spectrum signal rather than the conventional

29

Transmitter

Tx Data"

Add Signature

Inverse FFT

Channel

Forward FFT

Remove Signature

Sum Components J Rx

Data

Receiver

Figure 2.6: Block Diagram of an OFDM Spread Spectrum System

direct sequence signal opens up a number of possibilities:

• The transmitter can adjust the transmit spectrum in response to the

jamming conditions by varying the power of each of the carriers. If some

carriers are jammed, the transmitter can shift all the energy away from

those carriers.

• Coding can be used in place of simply sending the same data on all the

carriers. In essence a repetition code can be replaced by a much better

code.

• Inserting time diversity produces a transmitted waveform that is the

function of multiple data bits. Consequently, there are up to 2M dif-

ferent waveforms which are chosen depending on sequence of data bits

being sent. This property could make the signal more suitable for low

probability of detection and low probability of intercept (LPD/LPI)

applications.

The OFDM-SS system has some of the advantages of both DSSS and FHSS

30

systems and, what is more important, it provides an easy way to implement

the rate adaptation concept we discussed earlier.

2.2.3 Equalization of OFDM signals

In addition to ISI, OFDM signals experience an additional type of interfer-

ence called inter-channel interference (ICI). ICI occurs when orthogonality

between subcarriers is compromised, and subcarriers within the same OFDM

symbol interfere with each other. A multipath channel will produce both ISI

and ICI. Traditionally, a guard interval, called cyclic prefix, is used to sup-

press ICI and ISI when the channel echo duration is sufficiently small. A

cyclic prefix appends a copy of the last M samples of the transmitted block

to the beginning of the block, as shown in Figure 2.7. This makes the linear

convolution performed by the channel behave like a circular convolution [23],

resulting in no spectral leakage from one sub-carrier into the neighboring

bins, i.e. eliminating ICI completely. At the receiver, the cyclic prefix is

removed, and the received block is processed as usual. If the cyclic prefix is

made longer than the delay spread, then ISI is removed as well, since any

energy from the current symbol will only interfere with the cyclic prefix of

the next symbol.

Figure 2.7: Adding the Cyclic Prefix

To handle multipath fading, cyclic prefix is generally combined with dif-

ferential modulation scheme such as DPSK. Differential detection avoids the

need for phase recovery, which can be difficult in a fast fading environment.

31

It is simple to implement, and when used in conjunction with a cyclic prefix,

removes ICI and ISI without the need for adaptive equalization and training

sequences. The disadvantage is that DPSK suffers about a 3 dB penalty

compared to coherent demodulation. In DPSK, the information is carried by

the change in phase between two symbols, rather than the absolute phase.

It assumes that the channel does not change significantly over the two sym-

bols, and will perform the same phase rotation on both symbols. Thus, the

difference in phase will remain unchanged after passing through the channel,

even if the actual phase rotation is unknown. With OFDM, bits can either

be differentially encoded between bins on the same FFT block, or between

consecutive blocks using the same bin.

Equalization can be used instead of differential detection in conjuction

with the cyclic prefix. In this case, coherent detection can be performed and

the performance loss due to differential detection is removed.

The following is a brief overview of equalization techniques for OFDM

signals. As already noted, the OFDM modulator and demodulator can be

implemented using an IDFT and DFT, respectively. Samples of the OFDM

signal, generated by IDFT can be represented as

x(n)=Y;X(j,k)ei2*kn/N, (2.13) fc=0

where k refers to subcarrier order, j is time index and n is the sample number

of the OFDM symbol. iV is the length of the IDFT which is also the total

number of subcarriers. When samples x{n) are directed through a linear

channel, h(n), with additive noise d(n), the received samples, y(n) is,

y(n) = x(n)*h(n) + d(n). (2.14)

The receiver demodulates the received samples using a DFT. From (2.14)

the signal can be expressed in the frequency domain as

Y{k)=X(k)H(k) + D{k). (2.15)

32

Depending on the channel, the received and demodulated signal samples are

more or less distorted, i.e. Y(k) ^ X(k). An equalization function W(k) can

be introduced to compensate the channel effects.

X(k) = W(k)Y(k) = W(k)X(k)H(k) + W(k)D{k). (2.16)

The compensation coefficients of W(k) can be generated using a conven-

tional LMS algorithm and using a decision-directed structure, as illustrated

in Figure 2.8. The adaptive algorithm operates independently for each of the

2(i

* ()'

DFT

EM

Wm(k)© I Wm(k+1)

r Kg)-

Ym(k) A X(k)

n[x(k>]

Figure 2.8: Conventional Least-Mean-Squared (LMS) equalizer

individual subcarriers and is governed by,

X(k) = Wm(k)Ym(k),

where

and

e(k) = X(k) - U[X(k)}

(2.17)

(2.18)

Wm(k + l) = Wm(k) + 2tie(k)Y^(k). (2.19)

The same approach can be used for spread spectrum OFDM except that the

decision is made based on a decision variable found by coherently combin-

ing the energy from all the carriers. As a result, instead of working on a

33

subcarrier-by-subcarrier basis adaptation, the algorithm treats all the sub-

carriers as a group and the adaptation is governed by,

where,

and

X(k) = £ Wm(k)Ym(k), (2.20) m=0

i(k)=X(k)-U[X(k)), (2.21)

Wm{k + 1) = Wm(k) + 2txe(k)Y^(k). (2.22)

The conventional LMS algorithm is well suited for static or time invariant

conditions due to its slow convergence behavior. The dynamic channel and

interference conditions of the tactical PRN will require faster converging

algorithms [24, 25].

2.2.4 Rate Adaptive Schemes

To operate with a channel of variable quality, it is necessary to either design

the signal for the worst-case or make the signal adaptive. The non-adaptive

case is wasteful of system resources, i.e. bandwidth and/or power, since the

worst-case conditions will occur only a small fraction of the time. Adaptation

can take many forms, including adjustment of the transmit signal power and

changes in the signaling rate. Although transmission power control is a basic

technique to compensate for the received signal loss due to fading, it tends

to conflict with the LPI/LPD requirement for the tactical networks.

The most primitive adaptive modulation was first proposed by Cavers

as an alternative to the power control technique in a Rayleigh faded chan-

nel [26]. In this case, symbol rate is adaptively controlled according to the

received signal level. However, it requires very complicated hardware to gen-

erate various clock rates as well as to prepare transmitter and receiver filters

matched to the possible bit rates.

34

Another possible modulation parameter for adaptive modulation is the

number of constellation levels. Hanzo proposed a modulation level controlled

adaptive modulation using variable QAM [27]. The system has much lower

hardware complexity than the symbol rate controlled systems because the

same modem configuration can be employed for any number of modulation

levels. The concept of trading off user data rate with bit error performance

can be applied to both single-carrier and multi-carrier systems. Hanzo [28],

Goldsmith [29, 30], Sampei [31], Kalet [32], Czylwik [33], Wittke [34] and

Cioffi [35] have studied adaptive modulation for either the single carrier or

multi-carrier systems. Figure 2.9 illustrates the adaptive modulation concept.

Instead designing for the worst case situation, e.g. the fringe of the coverage

region in an AWGN channel, as in a fixed rate system, the adaptive system

varies its number of constellation levels according to the channel quality,

resulting in better utilization of the network resources.

OFDM is a bandwidth efficient multicarrier modulation scheme because

it allows the subcarriers to overlap spectrally. There has been considerable

effort to optimize the bandwidth utilization by studying the loading algo-

rithm uses to assign transmit bits to the individual subcarriers. The adaptive

modulators select from different QAM modulation formats, e.g. no modu-

lation, 2-PSK, 4-PSK, 8-QAM, 16-QAM, 32-QAM, 64-QAM, 128-QAM and

256-QAM based on the channel SNR conditions. This means that 0, 1, 2,

3, ...8 bits per carrier or per subcarrier can be transmitted. In each case

the constellation size of each individual carrier is adjusted independently in

accordance with the signal quality in its particular channel.

Most of the adaptive modulation schemes studied to date are oriented

toward a channel with a reasonably high signal-to-noise ratio {SNR). In

these systems, the users all agree to shutdown transmission when the chan-

nel SNR falls below some threshold. We propose to study the throughput

optimization problem in a low channel SNR dominant situation. Such a

35

Poor quality Region Moderate quality Region

A QPSK

Worst quality Region (Enlarged cover area)

Poor quality Region Moderate quality Region

Best quality Region

1/2-rate QPSK

A QPSK

■ 16QAM

© 32QAM

X 64QAM

Figure 2.9: Fixed rate system vs. adaptive system with variable

constellation

scenario prevails in military tactical networks where the channel is mostly

under jammer control and it also appears in commercial wireless networks

when mobiles are wandering in the cell coverage fringe areas. Other potential

applications exist, such as the power limited space and satellite communica-

tions. Our adaptive rate scheme builds upon OFDM-SS [21, 36] and, instead

of shutting down transmission at these poor SNR areas, it increases the pro-

cessing, thereby allowing the receiver to boost the despread SNR through

coherent combining of subcarrier energy.

36

2.3 Wireless Networks

2.3.1 802.11

We are all being exposed to a communications revolution that is taking us

from a world where the dominant mode of electronic communications was

standard telephone service and voiceband data communications carried over

fixed telephone networks, packet-switched data networks, and high-speed

local area networks to one where a tetherless and mobile communications

environment has become a reality.

Wireless networks can be categorized into voice-oriented and data-oriented

networks. The focus of this report is on data-oriented packet radio networks,

generally called wireless LANs (WLAN). WLANs are designed for local high

speed wireless communication among communication terminals. Its concept

was first introduced around 1980 [37, 38]. In the middle ofthat decade, the

ISM bands were released in the US [39, 40] for communications use. The

first WLAN products appeared in the market around 1990 [41, 42, 43] and

IEEE 802.11 standards work started shortly after that [44, 45]. Today, a

variety of technologies and several sectors of the market have been examined

for WLANs, and major international standards are evolving.

The IEEE 802.11 committee and the European Telecommunications Stan-

dard Institute (ETSI) RES-10 committee for HIPERLAN are developing

standards for physical and MAC layers of WLANs. IEEE 802.11 is focus-

ing on operation in the ISM bands and are restricted to spread spectrum

technology. For the 900MHz and 2.4GHz bands, WLANs use either direct

sequence spread spectrum (DSSS) or frequency hopping spread spectrum

(FHSS). Because of the advantages of OFDM, IEEE 802.11 standard com-

mittee has adopted OFDM as the modulation scheme for the 5GHz band and

OFDM is also targeted to be a common physical layer specification for the

worldwide band for license exempted devices. The ETSI's RES-10 consid-

37

ered decision feedback equalization (DFE), multicarrier modulation (MCM)

and sectored antenna systems (SAS) for the HIPERLAN, finally deciding on

DFE. MCM was not adopted for the HIPERLAN, presumably because of the

need for highly linear RF amplifiers which are difficult to build with the lim-

ited power available for PCMCIA add-ons. However, the area of minimizing

peak-to-average power ratio is currently very active and it is believed that

solutions to this problem will become available to avoid using highly linear

RF amplifiers for the OFDM systems.

DSSS is one of the adopted modulation techniques in the current IEEE

802.11 standard, though it is not used used with CDMA, but rather, with

Carrier Sense Multiple Access with Collision Detect (CSMA/CD). For the

2.4 GHz ISM band, the available bandwidth is 83.5 MHz. Most of the current

implementations of 802.11 use an 11-chip Barker code as the spreading se-

quence, providing only a small amount of processing gain. For a 1 MHz data

rate with binary phase shift keying (BPSK) or a 2 MHz rate with quaternary

PSK (QPSK), the single channel bandwidth is approximately 22 MHz. The

combination of signal and available bandwidth translates to three indepen-

dent channels in the 2.4 GHz ISM band. Actual implementations specify 8

partially overlapping channels in the band and force a given network to use

only one of the channels. Multiple channels are used to provide the capability

for multiple co-existing networks.

The performance of DSSS in fading channel is generally good if the band-

width of the spread signal is substantially greater than the coherence band-

width of the channel. The use of a RAKE [3] receiver structure further en-

hances the performance. One drawback of the DSSS/CDMA signaling is that

it may have difficulty operating in a mesh network, i.e. one supporting peer-

to-peer communication. The reason for the concern is that DSSS/CDMA

operates best with power control which minimizes or, ideally, eliminates, the

near-far problem. Imprecise power control greatly diminishes the capacity

38

of a DSSS/CDMA network by increasing the multi-user interference. Power

control is best utilized in a star network where all users are communication

with a central station which provides the power control information which

makes all the signals arrive at the same power level. Within a mesh network,

the varying distances between communicators makes effective power con-

trol at best very complicated and, more likely, impossible. DSSS has been

thought to be only for low- or medium-bit-rate transmission like kilobit-

per-second transmissions in some cellular systems and megabit-per-second

transmissions in ISM bands, since it requires much wider radio bandwidth

than data bandwidth. Assuming 156 Mb/s for asynchronous transfer mode

(ATM) transmission in a submillimeter- or millimeter-wave band, SS trans-

mission with Gp (processing gain) = 15 requires 2.325 GHz. Such broad

bandwidth does not seem realistic for a simple direct sequence (DS) method

for the following two reasons:

• Severe interchip interference occurs.

• It is difficult to synchronize such a fast sequence at a receiver.

Frequency hopping is another adopted modulation technique for the IEEE

802.11 standard. There are many variations of frequency hopping which

may be valuable for a channel with multipath fading and jamming. In one

case, the hopped carrier is a narrowband signal, such as a frequency-shift

keyed (FSK) signal. Fast frequency hopping, in which one symbol is spread

over multiple hops, and slow hopping in which one or more symbols are

transmitted at each hop frequency provide the frequency diversity needed to

combat multipath and narrowband interference.

In summary, all techniques have advantages and disadvantages. Direct

sequence has the advantage that processing gain (data rate) can be easily

varied but has the disadvantage of occupying the entire bandwidth, leaving

the receiver open to interference within any portion of the band. Frequency

39

hopping has the interference avoidance capability but it can be more difficult

to vary the data rate over a wide range. On the contrast, multicarrier modu-

lation, OFDM in particular, is a technique which has some of the advantages

of both direct sequence and frequency hopping. In this technique, multiple

carriers are used to send the message and, depending on how the carriers are

used, the resulting signal can be made to look similar to a direct sequence sig-

nal or a frequency hopping signal. A major advantage is that it is possible to

easily and rapidly change the signal characteristics, including the processing

gain. It is for this reason that there is considerable research activity oriented

toward using OFDM for the new generation wireless network standards.

40

Chapter 3

The RA-OFDM System

3.1 Introduction

Orthogonal frequency division multiplexing (OFDM) [14, 17] has received

considerable attention as a method to efficiently utilize channels with non-

flat frequency responses and/or non-white noise. In its most common form,

a high rate data stream is divided up among the many carriers in the system

in a manner which optimizes the capacity of the overall channel. OFDM can

also be used as a spread spectrum modulation (OFDM-SS) [18, 19, 20, 21]

wherein spectral spreading is accomplished by putting the same data on all

the carriers, producing a spreading factor equal to the number of carriers.

At the receiver, the energy from all the carriers is coherently combined to

produce the decision variable. Multiple users can be supported in the same

channel through Code Division Multiple Access (CDMA) [22]. In this case

each user has a unique signature sequence which determines the set of car-

rier phases. To receive a particular signal, the receiver needs to know the

signature sequence for that user in order to align the carrier phases for the

coherent combining operation.

The use of spreading with OFDM provides anti-jam capability as well as

41

enabling the use of CDMA. While resistance to jamming is clearly impor-

tant in a tactical network, the use of spreading tends to limit the available

throughput due to the bandwidth expansion. A main focus of this chapter

is the study of the performance of an OFDM system which makes it possi-

ble to vary the data throughput in response to channel conditions. When

anti-jam capability is needed, the signaling format is adjusted to increase the

spreading while, when the channel is clear, spreading is reduced to increase

the throughput. More specifically, in a favorable channel, the system would

operate much like the conventional OFDM system where different data bits

are transmitted on different carriers yielding high throughput. In a severe

interference channel, the system would operate like the OFDM-SS system,

sacrificing throughput to provide the needed processing gain to overcome

the jamming. In most cases, the system would operate between these two

extremes, providing sufficient processing gain to mitigate the channel effects

while maximizing throughput. We call this system rate-adaptive OFDM

(RA-OFDM). Figures 3.1 and 3.2 compare the conventional OFDM system

with a RA-OFDM system.

Bit 1 Bit N

IM frequency

1 CO 0-

i o T

w

IFFT FFT

CO

©

1 O

"55 1

CO 0-

Data Channel In

Data Out

Figure 3.1: Conventional OFDM System

The ultimate goal for the RA-OFDM system is to provide reliable com-

42

Bit 1 Bit 4

Data_ In

11 111 1 N=8-M=2ca5e M N/M

£ 75 CO Q. o

«i •c 03

CO

N/M 0) Q. a CD

5 IFFT FFT

K Q. CO

0)

0) > c

Sum —» (0 'C (U

03 A

"33

(0 a

Channel

Sum —-

M

Data Out

Figure 3.2: Variable Processing Gain OFDM

munications over a broad range of channel conditions through the adjustment

of the processing gain. Additive white Gaussian noise (AWGN), frequency-

selective Rayleigh fading and flat Rayleigh fading channels will all be consid-

ered and the emphasis is on developing a single adaptive strategy that will

apply in all cases. The focus of this chapter, then, is to demonstrate the

effectiveness of the RA-OFDM concept for each of the channel types and to

show that the adaptation scheme is of reasonable complexity.

Adaptivity of the proposed system stems from the easy manipulation of

the system processing gain. To allow an efficient application in a packet radio

network, the system should introduce minimum overhead for equalizer train-

ing, especially upon rate adaptation. In the following sections, we present

the RA-OFDM system which allows a smooth transition of processing gain

to track the changing channel conditions. Its use in a packet radio network

environment is discussed and simulation models are introduced. The perfor-

mance of the RA-OFDM system under AWGN, static multipath, frequency

selective fading and frequency-nonselective fading channels completely jus-

tifies the rate adaptation concept. The chapter concludes with an overall

system adaptation strategy which allows reliable communications in a broad

range of channel conditions, including AWGN, frequency-selective fading, fiat

fading and interference.

43

3.2 RA-OFDM Receiver

With OFDM modulation, variable throughput can be implemented by chang-

ing the amount of redundancy in the placement of data bits on the carriers.

For simplicity, assume initially that the data is not coded. The highest

throughput is accomplished by sending different data on each of the carriers.

This arrangement does not provide significant anti-jam capability nor does

it produce any frequency diversity to help mitigate the effects of frequency

selective fading. Inserting a processing gain of 2 requires that the same data

be sent on a pair of carriers, preferably spaced apart in frequency to produce

frequency diversity for both multipath and anti-jam protection. Increasing

the processing gain to 4 requires sending the same data on 4 carriers, a pro-

cessing gain of 8 requires sending the same data on 8 carriers, etc. The

maximum processing gain available equals the number of subcarriers in the

system.

In order to make the format adaptive, i.e. make the processing gain re-

spond to channel conditions, it is necessary to assume that the receiver will

feedback some information to the transmitter. This feedback is necessary be-

cause it cannot generally be assumed that the transmitter knows the channel

as seen by the receiver. Additionally, any changes made to the transmit

signal format must be accommodated by the receiver, meaning that the re-

ceiver must adapt its demodulation and detection operations to adjust to the

changes in the signal. The information that is returned can take many forms,

from a simple received signal quality measurement to detailed information

on the properties of the interference. For instance, if a fixed-frequency nar-

rowband jammer is present, the receiver may feed this information back to

the transmitter which can then avoid the use of carriers in the jammed fre-

quency band, shifting the transmit power to other carriers. In this chapter,

we will only consider the simplest case, where the transmitter changes the

44

processing gain of the transmitted signal on a packet-by-packet basis and the

receiver learns of these changes through the packet preamble. An example

packet structure will be provided later.

Multipath fading induces phase and amplitude variations in the subcarri-

ers. For flat fading, these variations are the same for all the carriers while for

frequency selective fading the variations are different for each carrier. There

are two common ways of dealing with the effects of this fading: differential

detection and equalization. With flat fading, differential detection can be

performed after the energy from the carriers is combined, since the fading

is the same for all carriers. In the more general frequency selective fading

case, however, differential detection must be performed individually on each

carrier before the combining operation. Since the signal-to-noise ratio on the

individual carriers is low when the processing gain is large, the losses due

to differential detection can be quite large in this case. In this chapter, we

will consider a receiver that uses equalization [46, 47] instead of differential

detection. While the equalizer can provide better performance, it may have

difficulty tracking rapidly changing fading or interference.

Figure 3.3 shows the RA-OFDM receiver which uses an equalizer to com-

pensate for channel effects. In the diagram, each summer has M inputs

(processing gain is M) and K symbols are sent simultaneously. M and K

will vary depending on the processing gain requirements but the product

MK will always equal the number of carriers. We have studied various fre-

quency domain adaptive equalizer structures in [21, 48]. Here we choose

the simplest one dimensional structure with only one layer of forward taps

to equalize the channel. Since simplicity is the utmost requirement for the

whole adaptive structure, it is coupled with the conventional cyclical prefix

approach [3, 49] to handle ISI and ICI mitigation. It is important that the

equalizer coefficients not need to be re-trained as a result of a change in

processing gain. The reason for this is that one possible operation scheme

45

involves training the equalizer at the highest processing gain using a packet

preamble and then changing the processing gain for the packet payload. This

is discussed in more detail in the next section. Since each complex equalizer

coefficient has a value that is a function of the channel, it is not dependent on

the spreading scheme and it is possible to have glitch-free switching between

processing gains.

Rx

Signal FFT

Signature

M-

-&-

^ash

zf Detected Data 1 (Variable Processing Gain)

El(k)

Periodic Equalizer

Training bits

Detected Data

(Variable Processing Gain)

Figure 3.3: Block Diagram of a RA-OFDM receiver with glitch-

free switching between processing gain. Here the processing gain

is M and K symbols are sent simultaneously.

46

3.3 Contrast with other Rate Adaptive Ap-

proach

In the following, we use an information theoretic approach to compare and

contrast our proposed RA-OFDM system with the adaptive modulation tech-

niques based on variable QAM. We will not only establish the similarity be-

tween the techniques, but also point out the advantages of our scheme as an

unifying modulation across a wide range of channel conditions.

The problem of optimizing channel capacity dates back to the 40's [50,

51, 52]. In the past decade, with the ever increasing need to provide very

high speed data communication over landline telephone network or wireless

media, this problem has received increased emphasis. Chapter 2 provided

an overview of many of the adaptive modulation techniques that have been

proposed.

3.3.1 Channel Capacity, AWGN Channel, High SNR

The multicarrier modulation system under consideration is shown in Fig-

ure 3.4. Throughout the analysis, we will use the following notation:

H(f): channel frequency transfer characteristic

W: total bandwidth of the multicarrier system

• N: total number of subcarriers of the multi-carrier system

• iV0/2: spectral density of additive white gaussian noise

• Pav: average transmitted power

Recall that the capacity of an ideal, band-limited, AWGN channel is:

•

•

C = Wlog2

47

P 1+ av

WN0

(3.1)

P. fi ni Wi

Modulator 1

P2 f2 nj W2

Modulator 2

PN f N nN WN

Modulator N

H(f)

N. 2

-<&

Pi=Power transmitted at ith subcarrier fi=Center frequency of ith subcarrier ni=Number of bits/symbol at ith subcarrier Wi=Bandwidth of ith subcarrier

Demodulator 1

Demodulator 2

Demodulator N

Figure 3.4: The multicarrier modulation system

where C is the capacity in bits/s. Consider a multicarrier system with a large

number of carriers spaced Af apart. If the total bandwidth is held fixed at

W, the carrier spacing will go to zero in the limiting case as the number of

carriers goes to infinity. In this system, the transmitted power P is divided

into the very large number of subcarriers, each one with power AfPk(f),

in which k(f) is the normalized power distribution. Each subchannel has

capacity:

Ci = A/log2 N0Af

and the bit rate becomes

l + -^Hf)\H(f)f A/log2 i+^(/)i#(/)r

Rb I, few log2 l + WHf)\H(f)\2

iVo df.

(3.2)

(3.3)

48

The optimized power distribution kopt{f) is found to be

*-<" =A" lüWUf {iA)

where

kopt(f)df = 1 few

P I,

and A is a Lagrange multiplier. The maximum bit rate, Ä6mflx is given by

RbmaX=[ log2(XK0\H(f)\2)df. (3.5) Jfew

This expression of the channel capacity of a linear filter channel with additive

Gaussian noise is due to Shannon. The basic interpretation of this result is

that the signal power should be high when the channel SNR is high, and low

when the SNR is low. This result is the so-called water-filling interpretation

of the optimum power distribution as a function of frequency.

Now, apply the Lagrange multiplier method to the case where QAM

modulation is used on the subcarriers. The transmitted signal consists of N

QAM carriers, each with a rectangular Nyquist spectrum of bandwidth equal

of Wi Hz. In the limit as Wt -* 0, we have an "infinite" multitone QAM

signal. Start with a relatively high channel SNR assumption so that we can

use a high level constellation size. According to Kalet [32], the bit rate Rb is

given by:

R, = i l0S2 JfeW

1 + T—7rü*£*w™l2

[Q-1 (&)] "° df, (3.6)

where Pe is the desired BER. K is a real constant such that 2 < K < 4 and

it is dependent on the constellation size, i.e. number of bits/symbol. Rb can

49

be tightly upper or lower bounded by choosing K equal to two or four. The

forward Q function is defined by

^if^'2* The optimized power distribution kopt(f) is found to be

k^f)=x'iümw' (3-7)

where

/ kopt(f)df = 1 Jfew /few

P

' I«"1 (*)] and A is a Lagrange multiplier. The maximum bit rate, Rbmax is given by

Rbma^f loga(AJfi|tf(/)|V- (3-8) Jfew

If we compare (3.5) and (3.8), we have essentially shown that, independent

of the shape of \H(f)\2, the degradation of the "infinite" multitone signal

to the capacity of any \H(f)\2 is the same and the degradation is solely

dependent on the factor . _JP ..a, i.e. the desired BER and modulation

constellation size. Let's verify this with an example of a flat channel response.

In this case, \H(f)\ = H and the optimum power distribution is

1 1 M/) = A--^j2= —

/ kopt(f)df = W*kopt(f) = l Jfew

50

and the optimum bit rate is

= [ log2 Jf€W

df

= W\og2

= W\og2

1 + KiH2

1 +

1 +

W

K,H2

W

PH2

df

= W\og2

3

1 + H2

iVn [<?-' (*)]' w

"^ [o-1 (*)] PJfJ2 is just the average power Pav, therefore,

(3.9)

Rbmax = Wl0g2 1 +

™M<K*)]J (3.10)

Now the degradation compared to the Shannon capacity can be easily found.

The basic formula for the capacity of the band-limited AWGN waveform

channel with a band-limited and average power-limited input is

p C = Wlog2 1 +

WN0. (3.11)

so the degradation term is . _XL^- For Fr(e) = 10 5, there is about 8.4

dB degradation in performance when comparing "infinite" multitone to the

Shannon capacity.

3.3.2 Channel Capacity, AWGN Channel, Low SNR

The adaptive QAM system works effectively in a high SNR situation. When

the channel is dominated by low SNR, this variable QAM system will simply

turn off transmission. We have taken a somewhat different approach to rate

adaptation in a multi-carrier framework. Our proposed RA-OFDM scheme

51

continues to transmit even in the poor SNR situation and it strives to ap-

proach the channel capacity within a performance gap determined solely by

the desired BER.

The RA-OFDM system is adaptive in that the amount of spreading, i.e.

the number of redundant carriers, is varied in response to channel conditions.

In addition to varying the number of redundant carriers, the constellation

size can be varied on the carriers, allowing high level QAM such as 64-QAM,

128-QAM or 256-QAM to be used to produce even higher throughput in

excellent channel conditions.

With BPSK and OFDM-SS modulation we have,

p- = Q (v2lp'j ■ (3-12)

where Ec and Pg are the chip energy and processing gain, respectively. Con-

sidering the overlapping nature of the multi-carriers, we find

n-%-Wö&W. (3.13)

When the channel is dominated by low SNR, Pg 3> 1, so rQ-uP m <C 1- Use

the approximation x ~ log2(l + x) when |a;| ■< 1 to obtain

Rb~Wlog2 (1+ ^_ [Q-l\Pe]]\

Denote Ts as the symbol duration and N as the total number of subcarriers.

With a little simplification we find

Ec PavTs/N PavTsW/N Pa. av

N0 N0 N0W WN0

and the bit rate becomes

(3.14)

2-, av

H» - HTlo«, | 1 + ^ä^_ | . (3.15)

52

Following the same Lagrange multiplier method that was used earlier, the

optimal throughput found to be,

" df. (3.16) Jfew Rh — I 1U&2 'few

1+wh?^mmf)f. Comparing this result to the previous one for the multitone QAM system,

there exists striking similarity between our proposed adaptive system and the

multitone QAM system. The degradation factor now is [Q-i(Pe)]2 instead of

? ,,,. Performance results for our system are shown in Figure 3.5. When [0-1(£)] the BER requirement is Pb = 10"5 the performance gap between the adaptive

processing gain system and the Shannon capacity is 9.59dB. When the BER

requirement is reduced to Pb = 10~3, the gap is reduced to 6.8dB. It is worth

pointing out that our proposed system continues to deliver throughput at

very low SNR while the multitone QAM system has to work in a much

higher SNR region.

The BER of coherent M-QAM with two-dimensional Gray coding over an

AWGN channel with perfect clock and carrier recovery can be approximated

by [29] BER ~ 0.2e_5(^T) (3.17)

in which 7 is the SNR and M is the number of constellation points. There-

fore, M = 256 for 256-QAM. Coupling this with a processing gain of 4, we

have

BER ~ O^e-^^5 ~ O^e"5^1) (3.18)

and we have essentially shown that a high level QAM with processing gain

delivers the same BER performance as a system with lower level QAM with-

out processing gain. If we can consider high level QAM as a special case of

spread spectrum system in which the processing gain is less than one, we have

a OFDM-SS system with variable processing gain across all channel SNR

conditions. Variable processing gain becomes a universal way to implement

adaptivity.

53

performance of adaptive processing gain system 10

N I •a

a 10 o

o Q.

W

10"

+ Shannon Capacity Pb=.00001

o Pb=.001

Gap between Adaptive System and Shannon Cap.=9.59dB, BER=.00001 Gap between Adaptive System and Shannon Cap.=6.8dB, BER-001

-20 -15 -10 -5 SNR in dB

10

Figure 3.5: Throughput of adaptive processing gain system, at low

SNR case

In summary, both the RA-OFDM system and the variable QAM sys-

tem mitigate signal quality degradation using additional redundancy as a

resource. In an AWGN or frequency non-selective channel, this redundancy

translates into higher effective "SNR" for the received signal. Variable QAM

is more often used in a wireline modem and operates on a higher SNR scale

than the RA-OFDM system. Due to the large power fluctuations in a wireless

channel, it is difficult to reliably demodulate signal sets with large numbers

of points without using complex equalization approaches. In addition to this,

the military applications generally require LPI/LPD. All of these means that

54

RA-OFDM system is more favorable in a tactical wireless application. Fur-

thermore, as will become clearer in the later sections, RA-OFDM scheme not

only boosts up the effective SNR seen by the receiver, but can also provide

additional diversity gain in a frequency selective channel, an advantage that

is not presented in other adaptive modulation schemes. It must be mentioned

that one of the fundamental characteristics of a communication link is the

possibility of a trade-off between bandwidth and power to obtain a specified

received signal power quality. Our proposed modulation scheme is especially

well suited for power limited links such as a mobile satellite system, while

the variable QAM scheme is more appropriate for bandwidth limited links

such as the landline modems.

3.4 Simulation Models

The RA-OFDM scheme is envisioned for use in a packet radio network.

An example packet structure that has a fixed number (1280) of symbols

as shown in Figure 3.6. The packet consists of unique words (UW) for pe-

riodic equalizer training (needed only for an equalizer-based receiver), data

rate indicator, optional FEC for the rate indicator and actual data symbols

transmitted. Except for the information symbols, all the other parts of the

packet are transmitted using the maximum level of processing gain to ensure

maximum error protection and to enable all receivers, including those with

poor channels, to attain packet synchronization. In all cases, accuracy of

the rate indicator is essential because received signal can not be correctly

demodulated unless the modulation parameters are correctly decoded. The

processing gain for the actual information bit stream depends on the channel

conditions. Note that in this scheme, if the structure of the OFDM signal,

i.e. the number of carriers and the carrier spacing remains unchanged, the

duration of each packet will depend on the processing gain that is used, even

55

though the number of symbols is held constant.

The variable rate system can operate in either either time division duplex

(TDD) or frequency division duplex (FDD) modes. With TDD, both base

station (BS) and mobile station (MS) transmit over the same RF channel,

but at different times. In this case both BS and MS experience similar chan-

nel fading conditions as their transmissions are typically half a TDD frame

apart. The transmission received by the MS is used to estimate the channel

integrity which then dictates the processing gain used by the MS transmit-

ter. Similarly, the transmission received by the BS enables the processing

gain levels used in the subsequent BS transmission to be determined. With

FDD, the uplink and downlink use different RF frequencies typically spaced

by more than the coherence bandwidth of the channel. Therefore the fading

on the two links may differ substantially. Both the BS and MS must monitor

their incoming channels and signal the required levels of processing gain by

the other in their transmission on their outgoing channels.

PACKET LENGTH.N =.1280 SYMBOLS

24 1156 ,100 (8%) (2%)

UW Rl

•H-.. (90%)

FEC (Optional)

DATA

UW: Unique Word for Equalization Training Rl: Data Rate Indicator

Rl=1, processing Gain=1 Rl=2, processing Gain=2

Rl=64, processing Gain=64

FEC: Error Correcting Code for Rate Indicator

DATA: Actual TX DATA (Variable processing gain)

^ Always at highest Processing Gain

J

Figure 3.6: Signal frame format for the RA-OFDM system

56

There are two criteria that can be used to judge the quality of the channel

by the receiver. One uses the Receive Signal Strength Indicator (RSSI) and

the other uses Bit or Word error rate. Both methods take advantage of the

fact that the fixed bit stream pattern for equalizer training are known by

both the transmitter and receiver. For RSSI switching mode, the average

magnitude of the baseband signal level over a frame provides an indication

of the short term channel path loss. For BER switching mode, as its name

implies, bit error rate is used as an indicator to the channel condition. Block

diagram of these two switching system is shown in Figure 3.7 for a TDD

application. A FDD system works in the same principle except a feedback

path is needed from receiver to transmitter.

The RA-OFDM system will be studied both analytically and through

simulation. The analytical model is used primarily to study the performance

in AWGN and flat fading channels while the simulation is used to validate the

analysis and to obtain performance results for the frequency-selective fading

channel. In all cases, perfect carrier and symbol synchronization is assumed

between the transmitter and receiver.

In the simulation, the RA-OFDM modulator with variable processing gain

and variable-rate coding, a number of channel models, and the rate adap-

tive receiver are implemented and used to perform Monte Carlo simulations.

The equalizer is adapted using either the conventional LMS algorithm in a

decision-directed mode or using perfect channel information. This later con-

dition is used to allow performance estimation without the introduction of

performance degradation due to imperfect equalizer tracking of the channel.

It also makes the result independent of the Doppler rate.

A number of different fading channels are considered analytically and im-

plemented in the simulation. The time-invariant multipath channel consists

of two equal-power rays with an inter-ray delay of 10 samples. The time-

varying frequency-selective fading channel model consists of multiple rays

57

spaced at sample intervals, Tc, and having a flat (uniform) intensity profile,

meaning that the mean power is the same for each of the rays. Each ray

is independently Rayleigh faded with an adjustable Doppler rate. With this

arrangement, an 8-ray channel will have a total delay spread of 8 samples, i.e.

8TC. The Rayleigh fading channel is modeled by an M-state Markov chain.

This concept of a finite-state Markov channel emerged from the early work

of Gilbert [53] and Elliott [54]. Wang extended the concept of the two-state

Gilbert-Elliott channel into the finite-state Markov channel [55]. The chan-

nel model is shown in Figure 3.8, where Si corresponds to the ith channel

state. The channel is in Si when the received SNR, 7, satisfies 7J_I < 7 < 7»

for some constant 7J_I and 7;. With BPSK signaling, the average channel

bit error probability for state i is

p[evror\i] = P Q(^)f^\i)dr (3.19)

/(7|?) is the conditional distribution of 7 given the channel is in state i and

it is given by 1 -SL- —e 7o

/(7|i) = f —, (3.20) e_7i_1/7o _ g-7i/7o v '

where 70 is the average SNR. Consider a system which transmits at a rate

of Rt symbols per second. The average transmission rate for state Si is

R\ = Rt* in (3.21)

symbols per second, where 7Tj is the probability that the channel is in state

i. According to [55], the average rate at which the received SNR passes

downward across the threshold 7$ is

Ni = J^fde-%, (3.22) V 7o

where fa is the Doppler frequency. The Markov transitional probabilities are

then approximated by TV-

Pi,i+i * 3T z = l,2,...M-l (3.23)

58

JVx * %i i = 2,3,...M and (3.24)

Pi,i — 1 - -Pi,2, -PM,M = 1 - PM,M-I

Ptii = l-Pi,i-i-Pi,i+i i = 2,3,...M-l

For the RA-OFDM system, the transmission rate at each state is different due

to the different processing gains. Therefore, R\ in (3.23) and (3.24) should

be further normalized with the actual bandwidth expansion factor for that

state. This Markov chain model is used to analyze the BER performance and

throughput of the RA-OFDM system. Various numbers of states are used

for the Markov chain.

Unless otherwise specified, the RA-OFDM signal consists of 64 carriers,

the FFT in the receiver has 64 bins and perfect symbol synchronization is

assumed, i.e. the blocks of the data processed by the FFT are time aligned

with the symbol intervals of the non-delayed path. Similarly, all processing is

performed at baseband, effectively assuming perfect carrier synchronization.

Random data is sent by the transmitter and binary signaling is used. For the

simulation, a minimum of 100 bit errors were recorded for each of the data

points and sufficient time was allowed for the equalizer to converge before

data collection began.

3.5 Results

3.5.1 AWGN and Time-Invariant Multipath Channel

We start by demonstrating the idea of rate adaptation using AWGN and

static two-ray channels. The two-ray channel model has inter-ray delay of

10 samples. Theoretical BER results for AWGN and simulation BER results

for the time-invariant two ray channel are shown in Figure 3.9. This figure

illustrates that, as the received SNR (i.e. the SNR before despreading)

59

varies from -12 dB to 12 dB, a bit error rate of 10~3 can be maintained by

appropriate control of the processing gain over a 24 dB range. Since the

number of carriers remains fixed at 64 and the carrier spacing is unchanged,

the throughput is being reduced each time the processing gain is increased.

Most of the degradation from the AWGN performance that is evident in the

multipath results is due to the fact that some of the channels are faded in

the later case. Note that the larger the processing gain, the smaller this

degradation due to the averaging effect of the despreading operation.

To test the actual rate adaptation scheme, we set up a dual rate system

in a packet radio network environment. Using the packet frame structure we

proposed earlier, 10 percent of each packet frame is dedicated to equalizer

training. In this scenario, the "good" channel always enjoys a 3dB SNR

advantage over the "poor" channel. In order to make up the SNR difference,

we use twice the processing gain for the "poor" channel as for the "good"

channel. The training is always performed with the maximum processing

gain and, in the "good" channel case, the processing gain is decreased during

the data transmission. The equalizer switches to decision directed mode

during the message portion of the packet. Figure 3.10 plots the system

performance under both channels as well as the BPSK theoretical results.

Keep in mind that Eb/N0 includes the benefit of the processing gain. As

expected, the system achieves very similar performance under the different

channels, which are both very close to the BPSK theory.

3.5.2 Rate Adaptation over Time-Varying Frequency

Selective Fading Channels

The frequency-selective fading channel can provide a diversity gain because

different portions of the frequency spectrum fade independently. The achiev-

able diversity D depends on the transmission bandwidth B and the coherence

60

bandwidth (A/)c and can be estimated roughly by [3],

D « B/(Af)c (3.25)

The total number of carriers is fixed at 64 and we use a deterministic fre-

quency interleaver which, if possible, separates the redundantly transmitted

bits by the coherence bandwidth (A/)c. Thus, the maximum amount of

frequency diversity is achieved. To concentrate on an accurate assessment

of diversity gain, we will use perfect channel information to determine the

equalizer coefficients as opposed to using an adaptive algorithm.

Figures 3.11 and 3.12 show the simulated BER versus Eb/N0 for 4-ray and

8-ray channels, respectively. In each case, the processing gain (spreading

factor) takes the values 1, 2, 4, 8, 16, 32 to 64 and coding is not used.

Note that the power of the AWGN scales with changes in the processing

gain. For a 4-ray channel, the achievable diversity as defined by (3.25) is

4. This fact is demonstrated in Figure 3.11 in which the BER performance

improves with increased processing gain until Pg = 4, at which point no

further gains are evident. The same conclusion holds true for the 8-ray model

in Figure 3.12 in which the performance improves until Pg = 8. Therefore,

for a typical mobile radio environment, the attainable diversity gain is limited

by the coherence bandwidth and overall bandwidth of the channel. Matching

the processing gain to the available diversity provides the best performance;

spreading further beyond this point does not provide additional diversity gain

but does still provide additional SNR gain. This latter point is evident if

BER is plotted against received SNR rather than Eb/N0.

To further demonstrate that diversity gain is a major contribution to the

performance gains attained with larger processing gain, the theoretical per-

formance curves for a diversity receiver using maximal-ratio combining are

shown in Figure 3.13 [3]. The number of independent Rayleigh fading chan-

nels is denoted by D = 1,2,4,8. Also shown are the simulation performance

61

results for the RA-OFDM receiver with 1-ray, 2-ray, 4-ray and 8-ray chan-

nels and when the processing gain matched to the channel, i.e. the processing

gain is set to the lowest value which fully takes advantage of the frequency

diversity. The simulation data matches the theoretical curve very well for

L < 4 because, in these cases, the L carriers for each bit undergo indepen-

dent Rayleigh fading. The simulation results do have a slight loss due to

energy loss for the cyclical prefix. For L = 8 the gap between the simulation

and ideal curve is larger, indicating that as the frequency spacing between

carriers carrying the same information bit gets smaller, the Rayleigh fading

becomes more statistically dependent, resulting in some loss in diversity gain.

3.5.3 Rate Adaptation over Frequency Non-selective

Rayleigh Fading Channels

With flat Rayleigh fading, the channel frequency response at any given in-

stant is flat across all the subchannels, meaning that diversity gain is not

available by simply spreading, interleaving and/or coding across the carri-

ers. Instead, time diversity must be obtained by using these techniques over

blocks of data that span many symbol intervals, i.e. many FFT blocks. The

slower the fading, the greater the needed time diversity and the less practical

this solution becomes. For example, consider a slow fading channel charac-

terized by 50Hz of Doppler frequency, yielding a coherence time, (Ai)c, of

~ 0.02s. If the sampling rate equals 1MHz and FFT block size is 64, achiev-

ing a two-fold diversity (in the time domain) requires an interleaver having

the size of 2 x .02/1 x 10~6 = 40,000 bits. In addition to the obvious storage

and complexity problems, the total delay resulting from the interleaver/de-

interleaver pair is 0.08s, a value that is much too high for most packet radio

network applications.

62

Figure 3.14 illustrates the problem with slow fading by showing the per-

formance of a Reed-Solomon (RS) coded OFDM spread spectrum system

under Rayleigh fading with various Doppler frequencies. The signal has 64

carriers, a sampling frequency of 1 MHz, uses a RS(63,32) coder and has a

processing gain of 16. The coding rate is justified in a later section. The

interleaver depth is equal to the size of the RS codeword, 378 bits. As a ref-

erence, theoretical curves for flat fading performance with no diversity (L=l)

and two-fold diversity (L=2) are also provided. Without using a very long

interleaver, the coded OFDM spread spectrum system can perform well in a

fast fading channel but not in a slow fading channel.

The RA-OFDM system approaches the flat fading problem by using cod-

ing and interleaving for fast fading channels and rate adaptation to track

channel variation in slow fading. In other words, in a fast fading chan-

nel, the rate will be adjusted to the average channel conditions and coding

and interleaving will be used to break up the fades while, in a slow fading

channel, the rate adaptation will follow the fluctuations the channel. The

coding and interleaving will remain when tracking the fading, it will just not

be depended upon to mitigate the fading. In the following, we will use the

finite-state Markov model for the Rayleigh fading to analyze the performance

of the RA-OFDM scheme and compare this performance to that for a fixed

rate system, i.e. a system which does not have variable processing gain.

The received signal SNR is partitioned into a finite number of intervals

corresponding to the total number of states. The thresholds are ordered as

0 < 7i < 72 < • • • < 1M < oo and these thresholds are chosen such that,

taking into account the processing gain for each particular state, a desired

BER of 1(T4 is obtained at these thresholds. As a result, the BER is always

less than or equal to 10-4 for all the channel states except S\. Since fading

in state Si can be arbitrarily deep, an infinite processing gain would be

needed to guarantee that the BER < 10~4. In the following, the adaptive

63

system adopts 2-state, 3-state and a 4-state adaptation models. The average

normalized throughput W with the adaptive transmission scheme is given by

M

w = Y.w^ (3-26)

where M is the number of adaptation levels, i.e. the number of states and

7Tj is the probability that the channel is in state i. W{ is the conditional

normalized throughput given the state is i, defined as the average number of

successfully transmitted information bits per unit time per unit bandwidth.

This quantity is given by

Wt = ft-yfl* (3.27) "si*

where PE\U Rc\i and Pg\i are the packet error probability, coding rate and

processing gain respectively, given channel is in state i. Figure 3.15 shows

the throughput of the RA-OFDM system as compared to a fixed rate system.

In this case, Rc\i is set to 1 for all i, meaning that all the redundancy is from

spreading only. It is clear from the figure that partitioning the channel SNR

into finite number of discrete states and matching the processing gain of

the RA-OFDM system to each of these states yields a huge improvement in

the system throughput. One reason for this improvement is that the fixed

rate system must be designed to provide the desired BER performance in

the worst-case channel conditions, meaning that it must incorporate a large

processing gain. Also, note that the performance of the adaptive rate system

gets better when the number of states increases. This improvement is due

to the fact that a closer match between processing gain and the channel

conditions is achievable.

The above model assumes there are no state transitions during a packet

duration. The following extends this model to allow at most one state tran-

sition during a packet duration under the assumption that the channel is

64

4 slowly varying. For example, if the packet length is 256 bits, fdT = 10

and 7Ti = 7T2 = 1/2, then the probability of two or more transitions occur-

ring in a packet duration is 0.0014, which can be ignored. The conditional

normalized throughput Wi is now given by

Wi = Wi]no state transition * Prob(™ state transition) +

^iione state transition * Prob(one state transition) (3.28)

A 2-state adaptation is used for illustration as in Figure 3.16. Transmission

rate in state 52 is twice of that in state Si. This factor has been considered

when calculating the transitional probabilities at each state. Throughput

contribution when there is no state transition is higher than the one when

there is one state transition. With the increase of Doppler frequency and/or

the number of states, the chance of state transition also increases. As a

result, the total throughput decreases. This degradation gets worse with

larger Doppler.

3.6 Discussion

The results that were presented show that, by adjusting the processing gain,

it is possible to maintain an acceptable BER over a wide range of channel

conditions. In the case of slow flat fading, being able to track channel vari-

ations provides a large gain in throughput since the link does not have to

be designed for worst-case conditions. Additionally, it is advantageous to

use FEC coding along with the processing gain. Analysis of the optimized

trade-off between FEC coding and spreading will be performed in Chapter

4. The proposed RA-OFDM uses a variable processing gain to deliver the

best achievable data rate on a packet by packet basis over AWGN and mul-

tipath fading channels. The system uses FEC to supplement the processing

65

gain, frequency domain interleaving to exploit any available frequency diver-

sity, and time domain interleaving to decorrelate any time domain variations

which are too rapid to handle through processing gain variation. The overall

adaptation strategy is to track variations in the channel whenever possible

within the constraints of the access method and the packet length. The best

approach is to adjust processing gain on a packet-by-packet basis, but this

may not be feasible in some cases. The depth of the time domain interleav-

ing would be determined by the limitations in the system's ability to track

channel variations since the main purpose of the interleaving is to "break

up" any fades that cannot be tracked. The ability to handle the slow fading

case through processing gain adaptation mitigates the need for large inter-

leaver depths, increases the overall throughput of the system and reduces the

possibility of a complete loss of signal.

66

\7

RX Front

End

RF Transmitter

Frame Parser

Extract Level of Processing Gain from start

of frame

Processing Gain Level

Variable Processing Gain Detector

-— Detected Data Bit

Receive Signal

Strength Measurement

Bit Error Rate Measurement

Switch Mode Control

Frame Packer

I

Variable Processing Gain Modulator

Encode level of Processing Gain at

Start of frame

User Data Bit Stream

Select level of Processing Gain at

Start of frame

Equalizer Training Pattern

Figure 3.7: Block diagram for RSSI and BER switching system

67

PM-I,M

S2 •

PM^-I

PM,M

Figure 3.8: M-state Markov chain modeling a Rayleigh fading chan-

nel

~i r-

*... *•..

_i i_

-25 -20 -15 -10 -5 0 channel SNR

10 15

Figure 3.9: Rate adaptation with cyclical prefix

68

0.1

0.01

$2 0.001 a

P4 kH o fcl

W *-» PQ 0.0001

le-05

le-06

BPSK Theory -< poor channel --< good channel ■■&■

4 5 6 7 Normalized Eb/NO in dB

10

Figure 3.10: Equalizer performance with realistic packet structure

69

0.1

0.01

SS

PS IM o fcl

W

S

0.001

0.0001

le-05

Spreading=l -»- Spreading=2 --*-- Spreading=4 ••&- Spreading=8 -*■••

- _=16 -*- Spreadlng=3i2^* •■ Spreading=64 -«*-

10 Eb/No in dB

12 14 16

Figure 3.11: BER performance for a 4-ray selective fading channel,

/D=50Hz

70

0.1

0.01 :

0.001

& d Pi

g 0.0001

«

le-05

le-06

le-07

~~-K---

Spreading=l -*- Spreading=2 -+-

tgading=4 -•&■ Spreadinl^S-ox

Spreading=16 -A- ^___Spreading=32 -*--

"Spreading=64 -■«■•

%, % "EJ

\ X

N.

10 12 Eb/No in dB

14 16

Figure 3.12: BER performance for a 8-ray selective fading channel,

/D=50Hz

71

0.1

0.01

0.001

3 a Pi

| 0.0001 W

s le-05

le-06

le-07

Spreading=l + Spreading=2 a Spreading=4 * Spreäämg5:„8_0

A

8 10 12 Eb/No in dB

14 16

Figure 3.13: Maximum achievable diversity from various channel

models

72

0.01

0.001

a o.oooi et

t-c

g w m le-05

le-06

le-07 14

Doppler=50Hz Doppler=100Hz Doppler=200Hz Theoretical L=l

^Theoretical L=2

+

16 18 20 22 24 26 Eb/NO in dB

28 30

Figure 3.14: Reed-Solomon coded OFDM spread spectrum system

in Rayleigh fading, FFT block size=64, (n,k) = (63,32), Pg=16

73

3 CX

60 3 p

T3

E O

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

04- 0

...x

,.B''

--■I—

.a-"

Fixed rate -*^ 2-state adaptation- '-+- 3-sat£ adaptation -s-

4:state adaptation ••*•

10 15 Channel average SNR in dB

20

Figure 3.15: Maximum normalized throughput with fixed rate and

RA-OFDM transmission schemes

74

3 O.

43 bü a p

O

0.25

0.2

0.15

0.1

0.05

0 «■

i (/

ß ' X''

,.-+--FrxetfTate ^frrr. - -f 2-stateadaptation,-fcl-50Hz -+—

_,2-<safe adaptation, fd=100Hz •&--" 2T&tateadap.tatiön';fä=200Hz •■•*

,Q''

X"

Channel average SNR in dB

Figure 3.16: Maximum normalized throughput with fixed rate and

RA-OFDM transmission schemes at different Doppler rate

20

75

Chapter 4

Adaptive Signaling with Packet

Radio Network

4.1 Introduction

In the last chapter, the focus was on the physical layer issues of the RA-

OFDM system. The emphasis of this chapter is to extend the analysis into

the data link layer of a packet radio network to demonstrate the effectiveness

of this rate adaptive signaling scheme.

The RA-OFDM system varies the processing gain and/or the modulation

constellation size according to the changing channel conditions, such as the

received signal-to-noise power ratio. This adaptivity results in users gaining

access to the channel at different bit rates depending on their local channel

conditions. The performance of a PRN using this signaling format is the

major focus of this chapter. We study the network throughput problem

under various access schemes. The advantage of adaptive system is first

illustrated in a downlink (base-to-mobile) using time division multiplexing

(TDM) scheme. It takes the best advantage of the adaptive system in terms

of throughput. In addition to the importance of this scheme in downlink

76

Channels, the maximum throughput derived from TDM can serve as a ceiling

benchmark for the proposed adaptive PRN with other access techniques. The

focus is then shifted to ALOHA and CSMA as these still are popular and

cost effective ways to handle uplink data traffic.

Classic pure ALOHA [56, 57, 58, 59] and CSMA system analyses [60, 61]

assume fixed length packets and Poisson arrival rates. In our adaptive system,

due to the variable processing gain and/or constellation sizes, the mobile

users transmit using variable packet durations with the number of data bits

per packet held constant. For example, in an Additive White Gaussian Noise

(AWGN) channel, the mobiles near the base station will have high SNR and

they can select a larger constellation size and/or lower processing gain to

shorten the packet duration. With the increase in packet success rate due

to fewer collisions, the overall system throughput is increased. On the other

hand, mobiles at the fringe of the coverage area are usually in worse channel

conditions and in order to combat the unfavorable conditions, data rate is

traded off for quality. Mobiles can select smaller constellation size and/or

larger processing gain. There are several papers [62, 63, 64, 65] studying

networks with variable packet lengths. However, none of these are applicable

to the adaptive system analysis because all of these studies assume constant

user data rate and packet lengths are independent of channel conditions. The

author introduces a method to analyze network throughput using variable

packet lengths due to variable user data rate. In addition, we incorporate the

packet error rate due to the AWGN into our analysis as in [66].

Given the built-in physical layer adaptivity of our proposed system, var-

ious network system parameters can be optimized. These can include net-

work throughput, total transmit power, traffic delay, network buffer memory,

traffic priority. For instance, in battery operated or Low Probability of In-

terception (LPI) driven applications, the goal could be to minimize transmit

power while subject to the BER constraint. For delay sensitive traffic, the

77

goal could be to maximize the throughput subject to delay constraint. For

variable priority traffic, the goal could be to ensure higher priority traffic to

get through with minimum BER. In this report, we focus only on network

throughput optimization subject to the desired BER constraint.

4.2 RA-OFDM System for Packet Radio Net-

works

This report is premised on the use of a physical layer that can adapt to the

channel quality in a way that maximizes the data rate while maintaining a

BER that is below a maximum acceptable level.

The proposed system selects the modulation parameters, specifically, the

processing gain, on a packet-by-packet basis according to the channel condi-

tions in order to achieve the maximum data rate while maintaining a desired

bit error rate. Figure 4.1 shows an example of the processing gain selection

procedure. In this example, BPSK and OFDM-SS modulation is used. Seven

different processing gains from 1 to 64 (doubling each step), corresponding

to seven user data rates, can be selected for a mobile user at any given time.

At a given SNR, a larger processing gain corresponds to a lower data rate

and a better BER performance. More importantly, a desired BER can be

maintained over a wide range of SNR values, e.g. a bit error rate of 10~3 can

be maintained over the range of -12 to +12 dB, by the appropriate control

of the processing gain (and data rate).

In this report we will be comparing the throughput performance of a

fixed rate system with an adaptive system. Refer to Chapter 3 for the packet

structure details.

78

10"

10" -20 -15 -10 -5 0

Channel SNR 10 15

Figure 4.1: Processing gain selection procedure

79

4.3 Throughput Analysis of the Adaptive Packet

Radio Networks

We have proposed an adaptive transmission scheme which transmits at a

higher information rate (i.e. lower processing gain) when the received SNR

is high, and a lower information rate (i.e. higher processing gain) when the

received SNR is low. With the underlying adaptive engine, we want to study

the networking aspects of the system.

4.3.1 Network Throughput Analysis, Downlink (base-

to-mobile) using TDM

The adaptive system achieves maximum throughput using a fixed access

scheme. A typical example involves the downlink capacity calculation using

time division multiplexing. We start the analysis by introducing an analytic

framework. This same framework is shared later for other contention-based

access schemes.

The network under study consists of a base station with mobile users in

a circular surrounding peripheral with radius R. Assume users are uniformly

distributed (in users/unit area) in the cell site. Therefore the probability

density function (pdf) of the user density is uniform in 9 and varies in the

distance from the center, r, as,

2 /(*,</) = ^, /M) = ^, f(r) = lo

2Wf(r,9)d9 —v.

Initially assume a free-space model where attenuation is proportional to

r2 [67] and assume that the processing gain is adjusted with respect to the

distance between the base station and mobile to maintain a constant BER.

To achieve this, divide the circular cell into seven rings, indexed from 1 at the

80

center to 7 at the edge. Assume for example that the maximum allowable

BER is 10"6, meaning that the fixed signaling format must provide BER

= 10~6 at the outer region and, consequently, will provide much lower values

for the inner rings. Conversely, the adaptive rate system strives to maintain

a fixed BER of 10~6 by using larger constellation size and/or less processing

gain for the inner rings, resulting in shorter packet durations. For easier

interface with the OFDM implementation, processing gain starts with 1 in

the most inner ring and doubles for each subsequent ring. In other words,

if % is the ring index from 1 to 7, then processing gain for each ring is 2J_1.

Based on the second order path loss model, in order to maintain a constant

received signal-to-noise ratio (after despreading) at each ring boundary, the

radius of ring i is Ri = Äi(-s/2)<-\ while R7 = R which is the cell boundary.

Given the above user population pdf function f(r), the probability that a

user is in ring i is thus fjj*^ f(r)dr. We will use this method again for other

user population profiles in the later section.

Tables 4.1 and 4.2 show parameters for the adaptive and fixed rate sys-

tems, in which JU, Pgt, ru Th Tputu Pk and BERi are the ring index, pro-

cessing gain, ring boundary, packet duration, individual throughput, proba-

bility user inside ring and bit error rate respectively.

Notice that the BER at each ring of the adaptive system is constant.

This is the result of variable processing gain. The BER is calculated at

the outer edge of each ring boundary meaning that the BER is generally

somewhat better than 10~6 and, therefore, the corresponding throughput

analysis produces a lower bound on performance. For the fixed rate system,

constant packet duration T and constant processing gain are used in all seven

rings. Therefore the BER in each ring decreases to virtually zero as a user

approaches the base station.

81

Table 4.1: Adaptive system parameters for seven-ring structure

Ri Pgi fi Ti Tpu^ Phi BERi

1 l R/8 T/64 64 1/64 io-6

2 2 fR T/32 32 1/64 IO-6

3 4 R/4 T/16 16 1/32 IO-6

4 8 4 •"- T/8 8 1/16 IO"6

5 16 R/2 T/4 4 1/8 10~6

6 32 #i? T/2 2 1/4 IO-6

7 64 R T 1 1/2 IO"6

Table 4.2: Fixed rate syst em parameters for seven-rin

Ri P& Ti T- Tputi Pk BERi

l 64 R/8 T 1/64 0

2 64 &R T 1/64 0

3 64 R/4 T 1/32 6.3 * 1(T81

4 64 ^R 4 ""- T 1/16 1.6 * 10"41

5 64 R/2 T 1/8 9.7 * IO"22

6 64 fa T 1/4 9.8 * IO"12

7 64 R T 1/2 10~6

■ring structure

Now consider a contention-free access scheme such as a TDM BS to MS

link and compare the throughput for the fixed and adaptive systems. Assume

that the transmission rate for both systems is C bits/sec at the fringe area

and very low BER is maintained so that we can neglect the packet errors due

to AWGN. Denote Si as the individual throughput from each ring, then the

82

maximum throughput in bits/sec for the fixed rate system is,

7

S'fixed = £ $ * -P™&(user in ring i) * C i=l

= (1/64 + 1/64 + 1/32 + 1/16 + 1/8 + 1/4 + 1/2) * C

= C (bits/sec)

For the adaptive counterpart,

7

Sadaptive = £ $ * Pro6(user in ring i) * C t=i

= (64/64 + 32/64 + 16/32 + 8/16 + 4/8 + 2/4 + 1/2) * C

= AC (bits/sec)

If we normalize the throughput with respect to the transmission rate of the

fixed system, the throughput of the fixed and adaptive system are 1 and 4

respectively, i.e. we get a potential four-fold increase in throughput using

our adaptive system.

Having users uniformly distributed over a circular region is not represen-

tative of many potential applications of a PRN. In a commercial application

like an indoor office environment, users tend to be clustered rather than uni-

formly distributed in two dimensions. One realistic population distribution

is along a building corridor. In such case, the previous assumption that user

population density linearly increases with distance from the hub is replaced

by a fiat, uniform density. In other words, the user pdf has changed from

y(r) = _^r into /(r) = i. The same distribution can be found in an outdoor

application such as coverage area along a highway. Figure 4.2 illustrates the

two user population profiles for a case of R = 100.

For the flat uniform density, the maximum throughput of the adaptive

83

0.02

0.018

0.016

0.014 c o 1 0.012 3

CO CO

I 0.01 >.

S 0.008 g Q.

0.006

0.004

0.002

+ 4- uniform in two dimension * * uniformin one dimension

**»*#*#*#$»##*****♦

_i i_

10 20 30 40 50 60 70 80 90 100 distance from base station, R=100

Figure 4.2: Linear versus flat user population profiles

system is

7

Sadaptive = ^ & * Proft(user in ring i) * C

= (64 * (1/8) + 32 * (N/2/8 - 1/8) + 16 * (1/4 - \/2/8)

+8 * (\/2/4 - 1/4) + 4 * (1/2 - \/2/4) + 2 * (>/2/2 - 1/2)

+1 * (1 - \/2/2)) * C

= 12.9C (bits/sec)

This result represents an almost thirteen-fold increase in system throughput.

Note that the throughput of the fixed rate system is not dependent on user

pdf, hence is again equal to C here.

Although there are some simplifications in the analysis for the downlink

capacity using TDM, it serves to illustrate the potential increase in capacity

84

offered by the adaptive scheme. Such a scenario is by no means unpractical,

since in applications such as wireless Internet services downlink capacity is

usually of great importance.

Next we will extend the same framework into uplink throughput analy-

sis. For data dominant traffic, random access schemes such as ALOHA and

CSMA are still the popular and cost effective access techniques and they are

the focus of the following sections.

4.3.2 Network Throughput Analysis for Pure-ALOHA

Adaptive PRN

In a pure-ALOHA system, mobile users randomly send their packets to the

central base station and wait for the return of a positive acknowledgement

upon the detection of an error-free packet. A user retransmits its packet if an

acknowledgement has not been received within a given period of time. Our

analysis uses the widely employed approximation of an infinite population of

users generating packets according to a Poisson process with parameter A,

e.g. [60, 61, 62, 63, 64, 65, 68, 69]. For the fixed rate system, all packet trans-

missions are of the same duration T. For the adaptive system, the actual

information bit rate changes with the channel conditions. This equivalently

translates into variable packet duration which depends on the channel condi-

tions. When observing the channel, packets (new and retransmitted) arrive

according to a Poisson process with parameter g packets/sec.

The channel throughput, S, is defined as the average number of packets

successfully transmitted in an interval of the packet duration. The parameter

G = gT is defined as the normalized offered load. Roberts [66] extended the

classic throughput analysis to include the effects of an AWGN channel,

S = Ge-2G(l-Ppe)(l-Pae) (4-1)

85

in which Ppe is the probability that a packet is not accepted due to channel

noise errors and Pae is the probability of acknowledgement error. If we fur-

ther simplify the channel to assume an error-free acknowledgement path, the

throughput is expressed as,

S = Ge-2G(l-Ppe). (4.2)

For our adaptive system, the throughput will be different in each ring.

We now calculate the expected throughput for a user in ring i. Denote the

transmission duration of the current user at ring i as U, and the period for

a collision user at ring j as tj. They are independent random variables.

The vulnerable window size is U + tj. Denote Si as the system throughput

conditioned on current user active in ring % and Pi, Pj as the probability that

the users are in ring i and j, respectively. Now,

Si = gTProb(no collision) (1 - Pbit error at ring J

7

Prob(no collision) = JJ Prob(no collision with user in ring j) J=I

= ft e-p^9{ti+t^ = e~sr+^7=1 Pjtj).

Keep in mind that independent of the data rate of the user, the successful

packet transmitted is N bits long. And since Pb is the probability of bit

error after despreading, the packet length in calculating packet error due to

AWGN is also N bits long.

Therefore, the total system throughput is

7

^adaptive = 2-~i ' *' V^-"/ i=l

The fixed rate system is a special case in which U = T for all i. If we plug

this into the above analysis, the fixed rate system throughput conditioned

86

on current user active in ring i is

&i fixed = dTe [1 - P^ error rate at ring i)

= Ge \1 — Pfoft error rate at ring i)

Therefore, the total system throughput is

7

dfixedrate — / , ^\ fixed *' i=l

the same result as the classic ALOHA analysis.

N

(4.4)

(4.5)

0.35 ' 1 1 ' ' ' ' ' ' T,T ' 1 '

+ #

+ + Rate adaptation * * fixed rate

0.3 -

0.25 I X -

CO o.2

Q.

t \ -

00

g ß 0.15 // \ \ -

0.1 \

0.05 / \

rSt * iHNl * ****** *'*'!

10~ IQ-' 10"' 10" offered toad G=g*T

10'

Figure 4.3: Throughput analysis, ALOHA system, moderate chan-

nel error, Pb = 10"6 at ring 7

Figures 4.3, 4.4 and 4.5 show the adaptive and fixed ALOHA system

throughput for different channel error rates. The packet length, N, is chosen

87

0.35 i i i ' i " + •

+ + Rate adaptation * * fixed rate

0.3 -

0.25 /\ -

(0 02 3 Q.

CO

H0.15 -

0.1 \

0.05

rS» m iü^lrsi * * * mm * » *■»■] 10"' 10- 10"

offered load G=g*T 10

Figure 4.4: Throughput analysis, ALOHA system, high channel

error, Pb = 1(T3 at ring 7, N=128

to be 1280 bits unless otherwise specified. Across all the loading conditions,

we see a consistent throughput performance improvement for the adaptive

ALOHA system. Note that when the BER is 10~3, N is reduced to 128 to

reduce the packet loss due to AWGN.

4.3.3 Pure-ALOHA, Different Path Loss Models and

User Population Profile

According to [67], both theoretical and measurement-based propagation

models indicate that the received signal power is proportional to f ^J , where

n is the path loss exponent which indicates the rate at which the path loss

88

0.3 -

+ + + Rate adaptation * » fixed rate

it *t* ****'*'* 10- 10"

offered load G=g'T 10'

Figure 4.5: Throughput analysis, ALOHA system, almost error

free channel, Pb = 10~12 at ring 7

increases with distance, r0 is the reference distance which is determined from

a measurement close to the transmitter, and r is the separation distance

between base and mobile. For the above results, free space propagation

(n = 2) was assumed. For a mobile radio channel, n is usually between 3 and

4 [70]. A larger value of n will increase the performance gain provided by the

adaptive system since the greater attenuation results in a larger data rate

disparity between the fixed and adaptive system at the inner rings. Figure 4.6

shows the improvement associated with various values of n.

Next we want to analyze system throughput under flat uniform user dis-

tribution. Such user profile is typical in an indoor office environment or an

outdoor highway situation. This distribution provides even more room for

89

0.45

0.4

0.35

0.3

(0 gO.25

0.2

0.15

0.1

0.05

x xx adaptive, path loss factor=4 O O o adaptive, path loss factor =3 + + + adaptive.path loss factor=2 * * * fixed rate

10"' 10" 10° offered load G=g*T

10

Figure 4.6: ALOHA system throughput with various path loss fac-

tors

throughput improvement with rate adaptation because the reshaping of the

pdf puts more users closer to the base station where the rate can be boosted

up. Figure 4.7 shows this improvement trend. Keep in mind that the fixed

rate system throughput does not depend on user population profile.

Figure 4.8 shows where the added capacity comes from by breaking down

the throughput contribution with respect to ring index for both the flat and

linear user profiles. It is obvious from the breakdown that the majority of the

throughput improvement comes from the inner rings where packet lengths are

much shorter resulting a much higher chance of getting through the network

without collision. The throughput at each ring of the linear profile increases

exponentially because of the population increases in the same way. Therefore,

90

0.45

0.4

0.35

0.3

CO 3 0.25

0.2

0.15

0.1

0.05

+ + + Rate adaptation, flat user profile O O o Rate adaptation, linear user profile * * • fixed rate

10" 10" offered load G=g*T

Figure 4.7: ALOHA system throughput with various user popula-

tion profile

not only does the uniform profile deliver a higher total throughput, it tends

to offer better fairness to users at each ring.

With the fixed rate system, once a user goes outside the fringe boundary,

the BER can become so high that a link can not be established or maintained.

This type of "hard boundary" is not acceptable for military applications and

can be undesirable in commercial applications. The adaptive system can

maintain connectivity for users outside the main coverage area by allowing

these users to use an even larger processing gain. If the adaptive system still

operates with the number of data bits per packet held constant, then the

packet duration increases, as users get further away from the base station.

As a result, supporting users outside the main coverage area could require

91

Figure 4.8: ALOHA system throughput breakdown with ring in-

dex, flat vs. linear user profile

even larger packet durations which can potentially become a major bottle-

neck to the system throughput. A long duration not only makes the long

packet itself difficult to get through, but also increases the chance of collision

with other shorter packets. One alternative is to reduce the bit rate of the

outside users by forcing fewer number of bits per packet for them. Another

one is to use a contention-free access scheme. There exists here, a balance

between continuing critical service for outside users and maintaining decent

throughput for inner users. The adaptive system is more flexible to maintain

this balance.

92

4.3.4 Network Throughput Analysis for Nonpersistent

CSMA Adaptive PRN

We now extend our network throughput analysis to nonpersistent CSMA.

We adopt a model similar to the one used in the ALOHA system and extend

the analysis in [61] to our adaptive system. Denote by r/2 the propagation

delay from the edge of the cell to base station and define o = T/T to be the

normalized propagation time. T is the transmission duration of a packet for

the fixed rate system. Thus, for a user at ring % ( with radius Ri ), delay of

T. = L + zRi/R will occur before all users hear its transmission.

We denote by B the duration of the busy transmission period, and by

B its mean. Let Ü be the time duration within the transmission period in

which a successful packet is being transmitted, with mean U. Let / be the

duration of the idle period with mean I. The cycle length is clearly B +1

and the throughput is given by

£, U^effective b~ B+I '

where Reffective is the effective data rate which is inversely proportional to

the processing gain and it accounts for the higher data rates for the inner

rings.

The idle period duration is the same as the duration between the end of

packet transmission and the arrival of the next packet. Because the packet

scheduling is memoryless, I is exponentially distributed with mean

* adaptive — — ■ V • / 9

The expected useful time U» given that the current user is active in ring

i, is given by

\ ti Successful period . „■. Ui = < , (4-7)

0 Unsuccessful period

93

If Psuc denotes the probability of successful transmission of a packet, and

P&_; is the BER at ring i, the conditional Ui is

Ui = E[Üi] = UPsucil-Pb-if

= tiProb(no packet arrives in [t, t + Tj]) (1 — Pb-i)

= Ue-™ (1 - Pb-i)N ■ (4.8)

To compute Bi, the average transmission duration at ring i, we want to

consider it as a "sum" of collisions with different numbers of contending

users, i.e. 0,1,2, • • -n contending users. Given a user starts transmitting at

time t, the vulnerable window is [t, t+ri\. The number of arrivals during that

window, including new and backlogged, follows the Poisson distribution, i.e.

(gTi)n

Prob(n arrivals in vulnerable window) = -—j—e 9n. (4.9)

What is a practical range for propagation delay T{? In most of our anal-

ysis, the packet size is chosen to be medium to large (N = 1280) in order to

fully utilize the adaptive advantage. Our system is targeted to high speed

indoor commercial/medium speed outdoor tactical applications. For an in-

door WLAN, we assume a minimum data rate of 1 Mbps. For a cell radius

of about 10,000 ft, this translates to a ~ 0.01. This value of a is also valid

for an outdoor application where the data rate is on the order of hundreds of

kbits/sec, so both the packet duration and propagation delay increase. Given

gri = a* gT ~ 0.01G, then for almost all the loading conditions of interest

( G < 102 ), gTi is small, and equation (4.9) approaches zero quickly as n

increases. Therefore we only consider lower order terms ( n=0 and 1) for the

majority of the loading conditions and a few higher order terms (n > 2) for

very heavy loading conditions. We will focus on the lower order terms for

the analysis now and verify that the approximation is very accurate later.

94

Denote Bi as the average transmission time given that user A starts trans-

mitting in ring i at time t, and that users B, C etc. potentially contend with

A. Then

Bi < e-9Ti*{tA + Ti)+gTi*e-9Ti*(max(tA,tB) + 2Ti) (4.10)

+higher order terms...

The right side is a upper bound because, t + Y denotes the time at which the

longest interfering packet was scheduled within a transmission period that

started at t and we are bounding Y with n. Since all the packet durations are

larger than ru the approximation is accurate. When there are two contending

users, max(tA,tB) in the second term of the equation, is the weighted average

over seven rings for user B given that user A is in ring i. The same reasoning

applies to the higher order terms.

Putting all these results together we can evaluate S* = UiReffective/(Bi +

/) and the system throughput

7

Sgdavtive ~ / , SjP\. (,4--'--U i=l

The fixed rate system is a special case in which all packets are of duration

T, therefore

Ifixed = - (4-12) 9

Uijixed = E[Ü] = Te-" (1 - Pb-if

and, since all U = T,

BiJixed^[T + 2ri}. (4.13)

Given /, Ut and Bh the system throughput can be evaluated. Figure 4.9 com-

pares the adaptive system performance with that for the fixed rate system.

95

As the figure shows, the approximation method using only the lower order

terms is accurate, especially for low to medium loading conditions. We will

continue to use this approximation unless otherwise specified. Figures 4.10

and 4.11 show the performance for various values of BER. Note that for

BER = 10-3, the packet length N is intentionally shortened to 128 and, and

correspondingly, the value a becomes 0.1.

1.6

+ + Adaptive CSMA, lower order terms only O O Adap. CSMA, higher order terms included * * Fixed rate CSMA

10 10' Offered load, G=g*T

Figure 4.9: Throughput analysis, CSMA system, moderate channel

error, P& = 10~6 at ring 7

For light loading, the throughput is almost equal to the offered load even

for the fixed rate system, so there is little room for improvement from adap-

tive system. As the load increases into the moderate area, we can see a

significant throughput increase from the adaptive approach, as the through-

put is nearly doubled. Once the load becomes too high, we can see that both

96

0.7

10'

+ + Rate adaptation, CSMA * * Fixed rate CSMA

10' 10 10 10 Offered load, G=g*T

10* 10=

Figure 4.10: Throughput analysis, CSMA system, high channel

error, Pb = 10-3 at ring 7, N=128

systems suffer a large performance degradation. This is typical for random

access schemes, however, the adaptive system degrades more slowly than the

fixed one.

Figure 4.12 shows the performance of these systems for various user pro-

files. Under the one dimensional flat user profile, the adaptive system delivers

about three times the throughput of its fixed rate counterpart. This increased

throughput occurs because more users now stay in inner rings where data

rate is much higher.

Paralleling the analysis of ALOHA, we plot the performance of the sys-

tem under various path loss models in Figure 4.13. Again, for mobile radio

channel, adaptive system can triple the system throughput compared to a

97

+ + + Rate adaptation, CSMA * * * Fixed rate CSMA

0.6

0.4

0t «»»»»»»«■ 10"3 10' 10" 10" 10

Offered load, G=g*T 10'

Figure 4.11: Throughput analysis, CSMA system, almost error free

channel, Pb = 10"12 at ring 7

fixed one.

Throughput versus normalized offered load, G, for various values of nor-

malized propagation time a is studied. Figure 4.14 shows these results for

a linear user profile while Figure 4.15 shows the results for a flat user pro-

file. As is expected, the lower a becomes the better the performance.

As a approaches 0, the system approaches a collision free situation. It is

very interesting to compare the system throughput for both the fixed rate

and adaptive system under such a circumstance. For the fixed rate system,

based on the above analysis, throughput approaches 1 matching the classic

NP-CSMA result of G/(G + 1). For the adaptive system, a -> 0 creates

a scenario very similar to the downlink capacity using TDM which we dis-

98

2.5

o1.5

0.5

+ + + Adaptive CSMA, flat profile O Oo Adaptive CSMA, linear profili * » * Fixed rate CSMA

10-* 10"' 10 10 10 Offered load, G=g*T

Figure 4.12: Throughput analysis, CSMA system, various user pro-

file

cussed earlier. Throughput approaches 4 and 12.9, respectively, under linear

and flat user profiles. These results match the maximum throughput results

we derived for the TDM cases. These observations are important. Based on

our earlier discussion of valid values for the normalized propagation delay

a, 0.01 corresponds to a cell radius of about 10,000 ft (about 2 miles). For

most indoor applications, cell sizes are much smaller, resulting in a much

smaller value for a. The same discovery can be also utilized in an outdoor

application to favor the pico-cells design in which o is intentionally kept very

small to improve capacity in high traffic areas.

99

3 1 ' I,I T] 1 | ■ I ' " "'"I" " T-n-rrrTT-

+ + adaptive.path loss factor=2 O O adaptive, path loss factor =3 X X adaptive, path loss factor=4

2.5 * * fixed rate -

2 ü <D

tn

-

JD C

2 1.5 Q. X O)

2

1- 1 ,

0.5

a=tau/T=0.01 \ >&*

oJ M» —■ **»*«■ ii 10' 10" 10'

Offered load, G=g*T 10' 10"

Figure 4.13: Throughput analysis, CSMA system, various path loss

model

4.4 Conclusion

In this chapter, we analyze the network throughput for an adaptive OFDM-

SS system. The system adapts the processing gain to the changing channel

conditions in order to achieve maximum throughput while maintaining de-

sired BER performance. Classical throughput analysis for both the fixed and

random access schemes is extended to study this adaptive system. The effect

of variable packet lengths due to variable user data rate as well as packet

error rate from AWGN has been incorporated into our analysis. System

throughput at the data link layer has been greatly improved compared to

conventional fixed rate system.

100

2.5

+ + adaptive. CSMA, a=0.01 o o adaptive. CSMA, a=0.0001 D o adaptive. CSMA, a=000001 V V fixed CSMA, a=.01 0 0 fixed CSMA,a=0.0001 » * fixed CSMA, a=0.000001

~r- 10" 10 Offered load, G=gN

Figure 4.14: Throughput-Load of CSMA under various propaga-

tion time, linear user profile

101

10

ß 6

+ + adaptive CSMA, a=0.01 0 o adaptive CSMA, a=0.0001 a D adaptive CSMA, a=.000001 V V fixed CSMA, a-01 0 0 fixed CSMA, a=0.0O01 • * fixed CSMA, a=0.000001

1^««»«»«»««»«»»»««»»««« 10"4 10~ä 10"' 10" 10'

Offered load, G=gN

Figure 4.15: Throughput-Load of CSMA under various propaga-

tion time, flat user profile

102

Chapter 5

Conclusion

This report makes several important contributions to the field of tactical

packet radio network designs. The major contribution is the development of

the rate adaptive spread spectrum OFDM system which achieves the ultimate

goal of maintaining a desired performance across a broad range of channel

conditions by the proper control of the system processing gain. Our adaptive

signaling is compared with other conventional adaptive modulation schemes

and it is shown to be a simple and universal scheme across large variation of

received signal quality. In particular, it is demonstrated to be especially well

suited for power limited link such as satellite communications and LPI/LPD

driven tactical applications. The rate adaptation strategy, associated with an

optimum combination of FEC coding and spreading, is shown to be practical

to implement and it has many potential applications for both commercial

and military communications. In addition, the RA-OFDM scheme is further

justified by analyzing the network throughput for a packet radio network. We

introduced a method to analyze network throughput using variable packet

lengths due to variable user data rate.

103

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